  We prove that if $A$ is a string algebra then there are not three irreducible
morphisms between indecomposable $A$-modules such that its composition belongs
to $\Re^{6} \backslash \Re^{7}$, whenever the compositions of two of them are
not in $\Re^{3}$. Moreover, for any positive integer $n \geq 3$, we show that
there are $n$ irreducible morphisms such that their composition is in
$\Re^{n+4} \backslash \Re^{n+5}$.
