A universal formula is proposed for predicting the site percolation threshold of two-dimensional matching lattices. The formula is slightly more accurate for these lattices than the formulas of Galam and Mauger, based on a comparison over a class of 38 lattices, and does not require two universality classes for two-dimensional lattices. The formula is constructed from the Galam-Mauger square root formula for site thresholds, by a modification which makes it consistent with the theoretical relationship between percolation thresholds of matching pairs of lattices. In the framework for evaluation of universal formulas introduced by Wierman and Naor, the formula is currently the best performing universal formula for site thresholds on this class of lattices.