Design of a linear systolic array for generating all combinations of m items out of n given items in a lexicographic order is presented. The algorithm of the systolic array is very simple only consists of two If-Then-Else statements. Its time complexity is O(2*n Cm 十m 一1)， and the required number of processing elements is m. This algorithm can be modified to generate all combinations of, at most m items out of n items. Also it can be combined with an m! generation algorithm to generate all the nPm permutations.