Linear filter banks with critical subsampling and perfect reconstruction (PR) property have received much interest and found numerous applications in signal and image processing. Recently, nonlinear filter bank structures with PR and critical subsampling have been proposed and used in image coding. In this paper, it is shown that PR nonlinear subband decomposition can be performed using the Gallois Field (GF) arithmetic. The result of the decomposition of an n-ary (e.g. 256-ary) input signal is still n-ary at different resolutions. This decomposition structure can be utilized for binary and 2k (k is an integer) level signal decompositions. Simulation studies are presented.