The classes of Reverse Jacket matrix [RJ]

and the corresponding Restclass Reverse Jacket matrix ([RRJ]

) are defined;the main property of [RJ]

is that the inverse matrices of them can be obtained very easily and have a special structure. [RJ]

is derived from the weighted hadamard Transform corresponding to hadamard matrix [H]

and a basic symmertric matrix D. the classes of [RJ]

can be used as a generalize Quincunx subsampling matrix and serveral polygonal subsampling matrices. In this paper, we will present in particular the systematical block-wise extending-method for {RJ]

. We have deduced a new orthorgonal matrix

.mem.[RRJ]

from a nonorthogonal matrix

.mem.[RJ]

. These matrices can be used to develop efficient algorithms in IMT2000 signal processing, multidimensional subsampling, spectrum analyzers, and signal screamblers, as well as in speech and image signal processing.gnal processing.g.