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We present a biorthogonal wavelet construction for Loop subdivision, based on the lifting scheme. Our wavelet transform uses scaling functions that are recursively defined by Loop subdivision for arbitrary manifold triangle meshes. We orthogonalize our wavelets with respect to local scaling functions. This way, the wavelet analysis computes locally a least squares fit when reducing the resolution and converting geometric detail into sparse wavelet coefficients. The contribution of our approach is local computation of both, wavelet analysis and synthesis in linear time. We provide numerical examples supporting the stability of our scheme.