An efficient and perfectly invertible signal transform featuring a constant-Q frequency resolution is presented. The proposed approach is based on the idea of the recently introduced nonstationary Gabor frames. Exploiting the properties of the operator corresponding to a family of analysis atoms, this approach overcomes the problems of the classical implementations of constant-Q transforms, in particular, computational intensity and lack of invertibility. Perfect reconstruction is guaranteed by using an easy to calculate dual system in the synthesis step and computation time is kept low by applying FFT-based processing. The proposed method is applied to real-life signals and evaluated in comparison to a related approach, recently introduced specifically for audio signals.