Recently, a new contactless Jc measurement technique by monitoring nonlinear responses from a coil mounted in the proximity of a superconducting film was reported by Classen et al. [Rev. Sci. Instrum. 62, 996 (1991)]. An improved method to measure the nonlinear inductive response is developed using an inductance bridge circuit, which discriminates the third-harmonic signal due to the nonlinearity from those of other origins. Moreover, in this technique, the phase of the third-harmonic signal can be used to determine the critical current.