Various phenomenological studies indicate that the mixing angle θK1 of K1A and K1B, the strange partners of the axial-vector mesons a1(1260) and b1(1235), respectively, lies in the vicinity of 35° or 55°, but whether this angle is larger or smaller than 45° still remains controversial. When the f1(1285)–f1(1420) mixing angle θP13 and the h1(1170)–h1(1380) mixing angle θP11 are determined from the mass relations, they depend on the masses of K1A and K1B, which in turn depend on the mixing angle θK1. We show that the approximate decoupling of the light qq¯ state from the heavier ss¯ state, which is empirically valid for vector, tensor and 3−− mesons, when applied to isoscalar axial-vector mesons, will enable us to discriminate different solutions of θP13 and θP11 and pick up θK1∼35°. Indeed, for θK1∼55°, the predicted θP11 disagrees sharply with the recent lattice calculation and the implied large ss¯ content of h1(1170) and qq¯ component of h1(1380) cannot explain the observation of their strong decays. We conclude that θK1 is smaller than 45°.