We present an efflcient algorithm for generating all maximum independent sets of a bipartite graph. Its time complexity is O (n sup 2.5 + (output size )), where n is the number of vertices of a given graph. As its application, we develop an algorithm for generating all maximum cliques of a circular-arc graph. When the graph is given in the form of a family of n arcs on a circle, this algorithm runs in O ( n sup 3.5 + (output size )) time.