One considers two strong homomorphisms, $\varphi$ and $\psi$. In Sec. 3 one finds a necessary and sufficient condition for the product $\varphi \psi$ to be a strong homomorphism. One also proves the following result: if $\varphi$ is surjective or$\psi$ is an isomorphism, then $\varphi \psi$ is a strong homomorphism. In Sec. 4 it is proved that any homomorphism can be split into the product of an isomorphism and a surjective strong homomorphism except for a particular case which is then determined.