This paper proposes a new class of 2D orthogonal symmetric wavelet filters using 2D nonseparable allpass filters. The proposed wavelet filters are based on the parallel structure of allpass filters with real-valued coefficients, which can be implemented with a low computational complexity and is robust to finite precision effects. The resulting wavelet bases are not only orthogonal, including perfect reconstruction (PR) condition, but also symmetric, whose analysis and synthesis filters have exactly linear phase response. It is also shown that the design problem of the proposed wavelet filters can be reduced to the phase approximation of the corresponding allpass filters. Therefore, it is easy to design this class of orthogonal symmetric wavelet filters by using the existing design methods of allpass filters. Finally, some examples are presented to demonstrate the effectiveness of the proposed orthogonal symmetric wavelet filters.