The authors present a new network structure that realizes perfect inversion networks (PINs) and perfect reconstruction networks (PRNs). In some applications, such as transform source coders, it is important that the cascade of the forward and the inverse transform give the identity exactly (perfect inversion), although the coefficients and the intermediate results are quantized. In subband coders, for example, the split and merge filter banks should preferably have perfect reconstruction. It is advantageous if perfect reconstruction can be accomplished even when the coefficients and the intermediate results are quantized. The proposed network has a ladderlike shape and a predescribed symmetry between the forward and inverse network or between the split and merge bank. In some parts of this ladder network almost any function is allowed. Due to the prescribed symmetry, the property of perfect inversion or perfect reconstruction is structurally assured.>