By analyzing the error of discrete hyper-wavelet transform Y = MX, we derive the relation between errors and eigenvalues of matrix MMT. Three new theorems about the eigenvalues of MMT are developed. Based on these theorems, a model for designing optimal biorthogonal wavelets is built. Optimal 8-8-tap and 9-7-tap filters for image compression are found by employing the model presented. Experiment has shown that the optimal 9-7-tap filters have better performance than Cohen and Daubechies' 9-7-tap wavelet for many images. Experiment has also shown that optimal 8-8-tap filters have better visual effects than optimal 9-7-tap filters.