Starting from the action of two coincident non-BPS D9-branes, we investigate kink configurations of the U(2) matrix tachyon field. We consider both Str and Tr prescriptions for the trace over gauge indices of the non-BPS action. Non-abelian tachyon condensation in the theory with Tr prescription, and the resulting fluctuations about the kink profile, are shown to give rise to a theory of two coincident BPS D8-branes. This is a natural non-abelian generalization of Sen's mechanism of tachyon condensation on a single non-BPS Dp-brane yielding a single BPS brane of codimesion one. By contrast, starting with the Str gauge trace prescription of the coincident non-BPS D9-brane action, such a generalization of Sen's mechanism appears problematic.