We expand on the automatic polarization‐based S‐wave‐arrival detection technique of Cichowicz (1993) and Diehl et al. (2009) to make it more effective for a broader range of distances and crustal structures. We use the characteristic function of Cichowicz (1993), which combines the polarization attributes of rectilinearity, directivity, and transverse‐to‐total‐energy ratio and, as does Diehl et al. (2009), modulates it with an amplitude weight function. Compared to Diehl, we increase the weight function exponent from 0.5 to 2, which stabilizes the characteristic function and emphasizes the S wave. We use the weight function by itself to determine if the signal‐to‐noise ratio is appropriate for picking and to determine a rough initial S pick. The pick is refined using the characteristic function. The picking algorithm works backward in time along the characteristic function from the initial pick until the characteristic function reaches a minimum. Using initial S picks based on the amplitude weight function, by increasing the weight function exponent and picking backward in time we avoid numerous incorrect early picks and drop traces with poor picking prospects. We apply the new approach to earthquakes in south‐central Tibet.