Abstract We consider the problem of computing the median of a bag of 2n numbers by using communicating processes, each having some of the numbers in its local memory. The memories are assumed to be disjoint. For two processes an algorithm is given. Its time and space complexity is linear while the communication complexity is 2 log 2 n. A lower bound of log 2 n on the communication complexity is derived. Thus the algorithm is optimal up to a constant.