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Wavelet analysis is a popular subject in science research. In this work, the concept of biorthogonal two-direction finitely supported wavelet packets with four-scale is introduced. A new method for designing two-direction biorthogonal wavelet packets is developed and their properties is investigated by means of time-frequency analysis method, matrix theory and operator theory. The decomposition relationship is established. Lastly, two Riesz bases of space L2 (R) are drawn from these wavelet packets.