In this paper we propose a new wavelet scheme for Loop subdivision surfaces. The main idea enabling our wavelet construction is to extend the subdivision rules to be invertible, thus executing each inverse subdivision step in the reverse order makes up the wavelet decomposition rule. As apposed to other existing wavelet schemes for Loop surfaces, which require solving a global sparse linear system in the wavelet analysis process, our wavelet scheme provides efficient (linear time and fully in-place) computations for both forward and backward wavelet transforms. This characteristic makes our wavelet scheme extremely suitable for applications in which the speed for wavelet decomposition is critical. We also describe our strategies for optimizing free parameters in the extended subdivision steps, which are important to the performance of the final wavelet transform. Our method has been proven to be effective, as demonstrated by a number of examples.