This paper addresses the analysis of the time-frequency technique so-called the second-order synchrosqueezing transform derived from continuous wavelet transform of multicomponent AM-FM signals. Such a technique is designed to deal with signals consisting of components (or modes) with strong frequency modulation . Before going into the details of this analysis, we revisit the case where the modes are assumed to be with weak frequency modulation as in the seminal paper of Daubechies et al. [1], but not assuming the wavelet is compactly supported in the Fourier domain. The remainder of the paper is devoted to the theoretical analysis of the second-order wavelet-based synchrosqueezing transform and to numerical simulations emphasizing the differences between this new synchrosqueezing transform and existing ones. An illustration of the benefits of using this new synchrosqueezing operator for the analysis of gravitational waveconcludes the paper.