We introduce a new adaptive transform for wavelet-based image coding. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. Since the adaptive transform is non-linear, we examine the central issues of invertibility, stability, and artifacts in its construction. We describe a new type of non-linearity: a set of linear predictors are chosen adaptively using a non-linear selection function. We also describe how earlier families of non-linear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.