Square-wave (SW) switching of the lasing direction in a semiconductor ring laser (SRL) is investigated using counter-directional mutual feedback. The SRL is electrically biased to a regime that supports lasing in either counter clockwise (CCW) or clockwise (CW) direction. The CCW and CW modes are then counter-directionally coupled by optical feedback, where CCW-to-CW and CW-to-CCW feedback are delayed by τ 1 and τ 2 , respectively. The mutual feedback invokes SW oscillations of the CCW and CW emission intensities with period T ≈ τ 1 + τ 2 . When τ 1 = τ 2 , symmetric SWs with a duty cycle of 50% are obtained, where the switching time and the electrical linewidth of the SWs can be respectively reduced to 1.4 ns and 1.1 kHz by strengthening the feedback. When τ 1 ̸ = τ 2 , asymmetric SWs are obtained with a tunable duty cycle of τ 1 /(τ 1 + τ 2 ). Highorder symmetric SWs with period T = (τ 1 + τ 2 )/n can also be observed for some integer n. Symmetric SWs of order n = 13 with period T = 10.3 ns are observed experimentally.