diff --git a/doc/ref/meataxe.xml b/doc/ref/meataxe.xml
index 2a7b7b88c5..ffdfd6e081 100644
--- a/doc/ref/meataxe.xml
+++ b/doc/ref/meataxe.xml
@@ -582,15 +582,47 @@ on all composition factors except number <A>nr</A>.
 <Section Label="meataxe:Invariant Forms">
 <Heading>MeatAxe Functionality for Invariant Forms</Heading>
 
-The functions in this section can only be applied to an absolutely irreducible
-MeatAxe module.
-
 <ManSection>
 <Func Name="MTX.InvariantBilinearForm" Arg='module'/>
 
 <Description>
 returns an invariant bilinear form, which may be symmetric or anti-symmetric,
 of <A>module</A>, or <K>fail</K> if no such form exists.
+
+<Example><![CDATA[
+gap> g:= SO(-1, 4, 5);;
+gap> m:= NaturalGModule( g );;
+gap> form:= MTX.InvariantBilinearForm( m );;
+gap> Display( form );
+ . 3 . .
+ 3 . . .
+ . . 2 .
+ . . . 1
+gap> ForAll(MTX.Generators(m), x -> x*form*TransposedMat(x) = form);
+true
+]]></Example>
+
+Since GAP 4.14 modules that are not absolutely irreducible are also supported:
+<Example><![CDATA[
+gap> g1:= GeneratorsOfGroup(SO(-1, 4, 5));;
+gap> g2:= GeneratorsOfGroup(SO(+1, 4, 5));;
+gap> m:= GModuleByMats(SMTX.MatrixSum(g1,g2), GF(5));;
+gap> MTX.IsIrreducible(m);
+false
+gap> form:= MTX.InvariantBilinearForm( m );;
+gap> Display( form );
+ . 3 . . . . . .
+ 3 . . . . . . .
+ . . 2 . . . . .
+ . . . 1 . . . .
+ . . . . . 3 . .
+ . . . . 3 . . .
+ . . . . . . 1 .
+ . . . . . . . 1
+gap> ForAll(MTX.Generators(m), x -> x*form*TransposedMat(x) = form);
+true
+]]></Example>
+
 </Description>
 </ManSection>
 
@@ -603,6 +635,42 @@ returns an invariant hermitian (= self-adjoint) sesquilinear form of
 <A>module</A>,
 which must be defined over a finite field whose order is a square,
 or <K>fail</K> if no such form exists.
+
+<Example><![CDATA[
+gap> g:= SU(4, 5);;
+gap> m:= NaturalGModule( g );;
+gap> form:= MTX.InvariantSesquilinearForm( m );;
+gap> Display( form );
+ . . . 1
+ . . 1 .
+ . 1 . .
+ 1 . . .
+gap> frob5 := g -> List(g,row->List(row,x->x^5));; # field involution
+gap> ForAll(MTX.Generators(m), x -> x*form*TransposedMat(frob5(x)) = form);
+true
+]]></Example>
+
+Since GAP 4.14 modules that are not absolutely irreducible are also supported:
+<Example><![CDATA[
+gap> g1:= GeneratorsOfGroup(SU(3, 5));;
+gap> g2:= GeneratorsOfGroup(SU(4, 5));;
+gap> m:= GModuleByMats(SMTX.MatrixSum(g1,g2), GF(25));;
+gap> MTX.IsIrreducible(m);
+false
+gap> form:= MTX.InvariantSesquilinearForm( m );;
+gap> Display( form );
+ . . 1 . . . .
+ . 1 . . . . .
+ 1 . . . . . .
+ . . . . . . 1
+ . . . . . 1 .
+ . . . . 1 . .
+ . . . 1 . . .
+gap> frob5 := g -> List(g,row->List(row,x->x^5));; # field involution
+gap> ForAll(MTX.Generators(m), x -> x*form*TransposedMat(frob5(x)) = form);
+true
+]]></Example>
+
 </Description>
 </ManSection>
 
@@ -617,6 +685,7 @@ or <K>fail</K> if no such form exists.
 returns a basis of the underlying vector space of <A>module</A> which is contained
 in an orbit of the action of the generators of module on that space.
 This is used by <Ref Func="MTX.InvariantQuadraticForm"/> in characteristic 2.
+Requires <A>module</A> to be irreducible.
 </Description>
 </ManSection>
 
diff --git a/lib/meataxe.gi b/lib/meataxe.gi
index 69d0cef90c..baa80b0260 100644
--- a/lib/meataxe.gi
+++ b/lib/meataxe.gi
@@ -3311,21 +3311,19 @@ end;
 ##
 #F  InvariantBilinearForm( module ) . . . .
 ##
-## Look for an invariant bilinear form of the absolutely irreducible
-## GModule module. Return fail, or the matrix of the form.
+## Look for an invariant bilinear form of the GModule module.
+## Return fail, or the matrix of the form.
 SMTX.InvariantBilinearForm:=function( module  )
    local DM, iso;
 
-   if not SMTX.IsMTXModule(module) or
-                            not SMTX.IsAbsolutelyIrreducible(module) then
-      Error(
- "Argument of InvariantBilinearForm is not an absolutely irreducible module");
+   if not SMTX.IsMTXModule(module) then
+      Error("Argument of InvariantBilinearForm is not a module");
    fi;
    if IsBound(module.InvariantBilinearForm) then
      return module.InvariantBilinearForm;
    fi;
    DM:=SMTX.DualModule(module);
-   iso:=MTX.IsomorphismIrred(module,DM);
+   iso:=MTX.IsomorphismModules(module,DM);
    if iso = fail then
        SMTX.SetInvariantBilinearForm(module, fail);
        return fail;
@@ -3368,41 +3366,24 @@ end;
 ##
 #F  InvariantSesquilinearForm( module ) . . . .
 ##
-## Look for an invariant sesquililinear form of the absolutely irreducible
-## GModule module. Return fail, or the matrix of the form.
+## Look for an invariant sesquililinear form of the GModule module.
+## Return fail, or the matrix of the form.
 SMTX.InvariantSesquilinearForm:=function( module  )
-   local DM, q, r, iso, isot, l;
+   local DM, iso;
 
-   if not SMTX.IsMTXModule(module) or
-                            not SMTX.IsAbsolutelyIrreducible(module) then
-      Error(
- "Argument of InvariantSesquilinearForm is not an absolutely irreducible module"
-   );
+   if not SMTX.IsMTXModule(module) then
+      Error("Argument of InvariantSesquilinearForm is not a module");
    fi;
-
    if IsBound(module.InvariantSesquilinearForm) then
      return module.InvariantSesquilinearForm;
    fi;
    DM:=SMTX.TwistedDualModule(module);
-   iso:=MTX.IsomorphismIrred(module,DM);
+   iso:=MTX.IsomorphismModules(module,DM);
    if iso = fail then
        SMTX.SetInvariantSesquilinearForm(module, fail);
        return fail;
    fi;
-   # Replace iso by a scalar multiple to get iso twisted symmetric
-   q:=Size(module.field);
-   r:=RootInt(q,2);
-   isot:=List( TransposedMat(iso), x -> List(x, y->y^r) );
-   isot:=iso * isot^-1;
-   if not IsDiagonalMat(isot) then
-     Error("Form does not seem to be of the right kind (non-diagonal)!");
-   fi;
-   l:=LogFFE(isot[1,1],Z(q));
-   if l mod (r-1) <> 0 then
-     Error("Form does not seem to be of the right kind (not (q-1)st root)!");
-   fi;
-   iso:=Z(q)^(l/(r-1)) * iso;
-   iso:=ImmutableMatrix(GF(q), iso);
+   iso:=ImmutableMatrix(module.field, iso);
    SMTX.SetInvariantSesquilinearForm(module, iso);
    return iso;
 end;
diff --git a/tst/testinstall/meataxe.tst b/tst/testinstall/meataxe.tst
index ee51f9a065..699b772915 100644
--- a/tst/testinstall/meataxe.tst
+++ b/tst/testinstall/meataxe.tst
@@ -1,4 +1,4 @@
-#@local G,M,M2,M3,M4,M5,V,bf,bo,cf,homs,m,mat,qf,randM,res,sf,subs,mats,Q,orig,S
+#@local G,M,M2,M3,M4,M5,V,bf,bo,cf,homs,m,mat,qf,randM,res,sf,subs,mats,Q,orig,S,g1,g2,form,frob5
 gap> START_TEST("meataxe.tst");
 
 #
@@ -105,6 +105,16 @@ gap> MTX.OrthogonalSign(M2);
 gap> SMTX.RandomIrreducibleSubGModule(M2); # returns false for irreducible module
 false
 
+# test invariant form detection on reducible module with two isomorphic
+# components (hence many automorphisms exist)
+gap> g1:= GeneratorsOfGroup(SU(4, 5));;
+gap> g2:= GeneratorsOfGroup(SU(4, 5));;
+gap> m:= GModuleByMats(SMTX.MatrixSum(g1,g2), GF(25));;
+gap> form:= MTX.InvariantSesquilinearForm( m );;
+gap> frob5 := g -> List(g,row->List(row,x->x^5));; # field involution
+gap> ForAll(MTX.Generators(m), x -> x*form*TransposedMat(frob5(x)) = form);
+true
+
 #
 gap> Display(MTX.IsomorphismModules(M,M));
  1 . . . .
@@ -254,8 +264,8 @@ gap> MTX.InvariantQuadraticForm( m );
 Error, Argument of InvariantQuadraticForm is not an absolutely irreducible mod\
 ule
 gap> MTX.OrthogonalSign( m );
-Error, Argument of InvariantBilinearForm is not an absolutely irreducible modu\
-le
+Error, Argument of InvariantQuadraticForm is not an absolutely irreducible mod\
+ule
 gap> mats:= GeneratorsOfGroup( SP( 4, 2 ) );;
 gap> m:= GModuleByMats( mats, GF(2) );;
 gap> Q:= MTX.InvariantQuadraticForm( m );