Figure 13. Animation of "ladies center while the men sashay," iterated twice.
This move is almost invariably called twice in a row. The net result is equivalent to "four men chain straight across" but will seem substantially easier to the dancers because women rarely perform the "courtesy turn" that any kind of chain move necessitates.

Women step forward.
Men sidestep clockwise until they reach the next man's position.
Women step back out to their original positions and all join hands.