The problem of outputting all parse trees of a string accepted by a context-free grammar is considered. A systolic algorithm is presented that operates in O (m n) time, where m is the number of distinct parse traces and n is the length of the input. The systolic array uses n2 processors, each of which requires at most O(log n) bits of storage. This is much more space-efficient than a previously reported systolic algorithm for the same problem, which required O (n log n) space per processor. The algorithm also extends previous algorithms that only output a single parse tree of the input.