Let D be a strongly connected balanced bipartite directed graph of order 2a≥8. In this note we prove: (i). If D contains a cycle of length 2a−2≥6 and max{d(x),d(y)}≥2a−2 for every pair of vertices {x,y}with a common out-neighbour, then for every k, 1≤k≤a−1, D contains a cycle of length 2k. (ii). If D is not a directed cycle and max{d(x),d(y)}≥2a−1 for every pair of vertices {x,y} with a common out-neighbour, then for every k, 1≤k≤a, D contains a cycle of length 2k unless D is isomorphic to a certain digraph of order eight which we specify.