In [1] L. Moser and W. Zayachkowski considered lattice paths from (0, 0) to (x, y) where the possible moves are of three types: (1) a horizontal step, (2) a vertical step, and (3) a diagonal step. They obtained an expression for the number of paths from (0, 0) to (n, n) lying below the main diagonal except at the terminal points. In this note we extend their results to cover any point (m, n) lying below the main diagonal.