Summary: The LCS problem is to determine the longest common subsequence (LCS) of two strings. A new linear space algorithm to solve the LCS problem is presented. The only other algorithm with linear-space complexity is by {\it D. S. Hirschberg} [Commun. ACM 18, 341-343 (1975; Zbl 0301.68042)] and has runtime complexity O(m n). Our algorithm, based on the divide and conquer technique, has runtime complexity O(n(m-p)), where p is the length of the LCS.