A new 2D sub-band coding scheme is proposed, 2D quadrature mirror filters (QMF) can be efficiently designed by a separable product of identical 1D QMF filters; Smith, Barnwell and Mintzer's 1D QMF design technique is carefully chosen and used in our 2D sub-band filters, the resultant 2D QMF filters and sub-band coder allow for "exact" reconstruction free of aliasing, phase and frequency distortion, these will be very useful for image sub-band coding applications.