The author introduces the notion of systolic communication, a general architecture technique for supporting efficient implementation of systolic algorithms. This notion is described and compared to the usual memory-to-memory communication. The Warp systolic array machine is shown to support the systolic communication. A processor array such as Warp that supports the systolic communication will be most effective in executing systolic algorithms, for which data move during computation. This is illustrated by a simple matrix multiplication example. Advantages of the systolic communication are summarized.