  In a recent work [Potter and Lee, Phys. Rev. Lett. 105, 227003 (2010)], it
was demonstrated by means of numerical diagonalization that the Majorana end
states can be localized at opposite ends of a sample of an ideal spinless
p-wave superconductor with the strip geometry beyond the strict one-dimensional
limit. Here we reexamine this issue, and study the topological quantum phase
transition in the same system. We give the phase diagrams of the presence of
Majorana end modes by using of $Z_{2}$ topological index. It is found that the
topological property of a strip geometry will change in an oscillatory way with
respect of the sample width.
