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In [2] the authors gave a constructive proof of the Brouwer fixed point theorem by means of a homotopy (continuation) method. The basic idea used in the proof is the concept of transversality; other applications were also given using this idea. In 7~ and [8] actual numerical computations based on our method were shown. In particular, in L8] a nonlinear boundary value problem, which had not been solved previously by standard schemes, was numerically solved. Recently the same idea was used in [5] to find all the d complex roots (counting multiplicity) of ad th order polynomial in a single unknown. The purpose of this paper is to show that ideas and techniques from transversality theory may again be used to find numerically all the zeros of a system of n polynomial equations in n unknowns.