  In a one-dimensional spinless p-wave superconductor with coherence length
\xi, disorder induces a phase transition between a topologically nontrivial
phase and a trivial insulating phase at the critical mean free path l=\xi/2.
Here, we show that a multichannel spinless p-wave superconductor goes through
an alternation of topologically trivial and nontrivial phases upon increasing
the disorder strength, the number of phase transitions being equal to the
channel number N. The last phase transition, from a nontrivial phase into the
trivial phase, takes place at a mean free path l = \xi/(N+1), parametrically
smaller than the critical mean free path in one dimension. Our result is valid
in the limit that the wire width W is much smaller than the superconducting
coherence length \xi.
