  The $N$-soliton solution is presented for a two-component modified nonlinear
Schr\"odinger equation which describes the propagation of short pulses in
birefringent optical fibers. The solution is found to be expressed in terms of
determinants. The proof of the solution is carried out by means of an
elementary theory of determinants. The generalization of the 2-component system
to the multi-component system is discussed as well as a (2+1)-dimensional
nonlocal equation arising from its continuum limit.
