In the present paper we show a new algorithm for random generation of boolean square invertible matrices nxn. This algorithm has, as initial parameter, a randomly selected boolean matrix A={ai,j}nxn , which has as the only restriction that there is not any I∈ {1…n}, such that ai,i = ai,i+1 = … ai,n = 0. The program is presented in the Mathematic language. [ABSTRACT FROM AUTHOR]