Let $M_n=M(n, F_q)$ be the semigroup of all $n\times n$ matrices over the field $F_q$ of $q$ elements. By using Dickson's invariants we construct a complete set of $q^n$ distinct irreducible $F_q[M_n]$ modules, called $H_{\beta}$ and give isomorphisms between them and the modules $F^{\alpha}$ which were constructed in [3] by the ''Weyl module'' construction.