This paper shows the existance of binary pseudowavelets, bases on the binary domain that exhibit some of the properties of wavelets, such as multiresolution reconstruction and compact support. The binary pseudowavelets are defined on % n (binary vectors of length n) and are operated upon with the binary operators logical and and exclusive or. The forward transform, or analysis, is the decomposition of a binary vector into its constituant binary pseudowavelets. Binary pseudowavelets allow multiresolution, progressive reconstruction of binary vectors by using progressively more coefficients in the inverse transform. Binary pseudowavelets bases, being sparse matrices, also provide for fast transforms; moreover pseudowavelets rely on hardware-friendly operations for efficient software and hardware implementation.