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This paper analyses the rule of the base vector arrangement for slant transform, gives the equations and the fast algorithms for the slant transform of arbitrary order 2/sup n/ with base vectors arranged in sequency increment, and makes traditional slant transform theory more consummate. Using this algorithm to image compression, the data entropy in the transform domain approaches that of the commonly used DCT but the operation speed is faster. This algorithm is suitable for the orthogonal transformation where high speed and hardware implementation are required. The fast algorithm of slant transform with sequency increment is extensively adopted in the other digital signal processing applications.