Wavelets and Wavelet Transforms have been studied extensively since the 1980′s. It has been shown that the Discrete Wavelet Transform (DWT) can be applied to an enormous number of applications in virtually every branch of science. The DWT is used for decomposing and reconstructing infinitely long signals. In practice, we only need to deal with finitely long signals, which raises the very important question of handling boundaries. We present how to handle boundaries by constructing endpoint functions and analyzing their properties.