This paper revisits the scheduling problem on an unbounded parallel batch machine for minimizing a maximum cost fmax. It was reported in the literature that the decision version of the problem is solvable in O(n2+nlogP) time, where n is the number of jobs and P is the total processing time of jobs. This implies that the optimization version for minimizing fmax can be solved in weakly polynomial time. But a strongly polynomial-time algorithm has not been provided for this problem. In this paper, we present an O(n4)-time algorithm for the Pareto optimization problem for minimizing Cmax and fmax, where Cmax is the maximum completion time of jobs. Consequently, the problem for minimizing fmax can also be solved in O(n4) time.