diff --git a/doc/Doc.autodoc b/doc/Doc.autodoc
index 611e187..684ecfe 100644
--- a/doc/Doc.autodoc
+++ b/doc/Doc.autodoc
@@ -5,6 +5,9 @@
 @Subsection A category of module homomorphisms
 @InsertChunk CategoryOfRepresentations
 
+@Subsection One step in the direct sum decomposition
+@InsertChunk DecomposeOnceByRandomEndomorphism
+
 @Subsection Another category of module homomorphisms
 @InsertChunk RepresentingC4C4
 
diff --git a/examples/DecomposeOnceByRandomEndomorphism.g b/examples/DecomposeOnceByRandomEndomorphism.g
index 3488798..05bd498 100644
--- a/examples/DecomposeOnceByRandomEndomorphism.g
+++ b/examples/DecomposeOnceByRandomEndomorphism.g
@@ -1,4 +1,4 @@
-#! @Chunk DecomposeOnceByRandomEndomorphism
+#! @BeginChunk DecomposeOnceByRandomEndomorphism
 
 LoadPackage( "CatReps" );
 
@@ -22,9 +22,9 @@ DecomposeOnceByRandomEndomorphism( nine );
 #! fail
 #! @EndExample
 
-#! The above shows that our representation nine is indecomposable.
+#! The above shows that our representation <C>nine</C> is indecomposable.
 #! We use the tensor product to generate another representation
-#! fortyone, that is hopefully decomposable.
+#! <C>fortyone</C>, that is hopefully decomposable.
 
 #! @Example
 fortyone := TensorProductOnObjects( nine, nine );
@@ -221,11 +221,12 @@ Display( S );
 #! A morphism in Category of matrices over GF(3)
 #! @EndExample
 
-#! Comparing the matrices of fortyone with those of S, we see
-#! that after decomposing once, we have seperated one small
-#! matrix on the diagonal: A $3\times 3$-matrix from $S(kq.a)$,
-#! a $3 \times 1$-matrix from $S(kq.b)$ and a $1\times 1$-matrix
-#! from S(kq.c). This matches with the sources of the 
+#! Comparing the matrices of <C>fortyone</C> with those of 
+#! <C>S</C>, we see
+#! that after decomposing once, we have separated one small
+#! matrix on the diagonal: A $3\times 3$-matrix from <C>S(kq.a)</C>,
+#! a $3 \times 1$-matrix from <C>S(kq.b)</C> and a $1\times 1$-matrix
+#! from <C>S(kq.c)</C>. This matches with the source of the 
 #! natural transformation $\iota$.
 
 #! @Example
@@ -246,7 +247,50 @@ Display( iota );
 #!  . . . . . . . . . . . . . . . 1
 #! 
 #! A split monomorphism in Category of matrices over GF(3)
-Source( iota(kq.1) );
-#! <A vector space object over GF(3) of dimension 3>
-Source( iota(kq.2) );
-#! <A vector space object over GF(3) of dimension 1>
+Display( Source( iota) );
+#! An object in The category of functors: Algebroid generated by the
+#! right quiver q(2)[a:1->1,b:1->2,c:2->2] -> Category of matrices
+#! over GF(3) defined by the following data:
+#!
+#! Image of <(1)>:
+#! A vector space object over GF(3) of dimension 3
+#! 
+#! Image of <(2)>:
+#! A vector space object over GF(3) of dimension 1
+#! 
+#! Image of (1)-[{ Z(3)^0*(a) }]->(1):
+#!  . 2 .
+#!  1 2 2
+#!  . . 1
+#! 
+#! A morphism in Category of matrices over GF(3)
+#! 
+#! 
+#! Image of (1)-[{ Z(3)^0*(b) }]->(2):
+#!  2
+#!  1
+#!  .
+#! 
+#! A morphism in Category of matrices over GF(3)
+#! 
+#! 
+#! Image of (2)-[{ Z(3)^0*(c) }]->(2):
+#!  1
+#! 
+#! A morphism in Category of matrices over GF(3)
+#! @EndExample
+
+#! We can then look at the other factor of the direct sum 
+#! decomposition, i.e. $\kappa$. The iteration of 
+#! <C>WeakDirectSumDecomposition</C> will continue then
+#! with <C>Source( kappa )</C>. Each time the random
+#! endomorphism will decompose the representation by
+#! at most a dimension of $3$.
+
+#! @Example
+Source( kappa );
+#! <(1)->22, (2)->15; (a)->22x22, (b)->22x15, (c)->15x15>
+result2 := DecomposeOnceByRandomEndomorphism( Source( kappa ) );
+#! [ <(1)->3x22, (2)->3x15>, <(1)->19x22, (2)->12x15> ]
+#! @EndExample
+#! @EndChunk