The interaction between the intersecting noncommutative D-branes (or
membranes) is investigated within the M(atrix) theory. We first evaluate the
spectrum of the off-diagonal fluctuation and see that there is a tachyon mode,
which signals the instability of the intersecting branes. We next explain in
detail how the tachyon modes (which are the off-diagonal fluctuations) can be
combined with the original branes (which are the diagonal elements) to become a
new diagonal matrix, which then represents the new recombined configurations
after the tachyon condensation. The tachyon condensation configurations of the
noncommutative branes we find are different from those of the commutative cases
studied in the previous literatures.