We describe a new type of sufficient condition for a balanced bipartite digraph to be hamiltonian. Let D be a balanced bipartite digraph and x,y be distinct vertices in D. {x,y} dominates a vertex z if x→z and y→z; in this case, we call the pair {x,y} dominating. In this paper, we prove that a strong balanced bipartite digraph D on 2a vertices contains a hamiltonian cycle if, for every dominating pair of vertices {x,y}, either d(x)≥2a−1 and d(y)≥a+1 or d(x)≥a+1 and d(y)≥2a−1. The lower bound in the result is sharp.