Each woman steps into the square and turns to the right (thus facing her corner).
She walks past her corner (passing to the left) and turns 180 degrees clockwise to face his back.
All men simultaneously walk directly across the square and turn 180 degrees clockwise to face the women.
All women simultaneously walk directly across the square a few steps behind the men.
When the women meet the men, couples "slide through"--a maneuver that exchanges their positions while rotating the women 90 counterclockwise and rotating the men 90 degrees clockwise.
Couples promenade counterclockwise (the direction they are now facing) until the woman reaches her starting position, at which point the couples pivot to face into the square.
This entire sequence is repeated three more times, thereby returning all men (who by this point will have traversed the entire cycle) to their home positions.