Let $\Zn$  be  a multitype branching process in a random environment
    (MBPRE)  which grows to infinity with positive probability for almost all
    environmental  sequences.   Under some conditions involving the first two
    moments  of  the  environmental  sequence,  it is shown that dividing the
    $\Zn$'s  components by their environment conditioned expectations yields a
    sequence convergent in $L^2$ to a random vector with equal components.