An efficient algorithm is presented for solving the min-max two-box problem in arbitrary dimension d≥2. The runtime of the algorithm is O(n log n+nd-1). For the plane, the algorithm is simpler than that of Glozman et al. since the only data structure used in the algorithm is a list and it runs in O(n) time after O(n log n) presorting step. The efficiency of the algorithm is based on the monotonicity of the evaluated function in the problem.