In this article, we introduce the concept of fractional wavelet transform. Using a two-channel unbalanced lifting structure it is possible to decompose a given discrete-time signal x[n ]s ampled with periodT into two sub-signals x1[n ]a ndx2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p +1 /q = 1. The low-band sub-signal x1[n] comes from [0 ,π /p ]b and and the high-band wavelet signal x2[n] comes from (π/p, π] band of the original signal x[n]. Filters used in the lifting structure are designed using the Lagrange interpolation formula. It is straightforward to extend the proposed fractional wavelet transform to two or higher dimensions in a separable or non separable manner.