Abstract: The symmetric property and compact support are incompatible for orthogonal wavelets in function space, whether the properties of discrete orthogonal wavelets can be compatible is still unknown. This paper proves that both the interpolating property and the symmetric property are incompatible with finite length for discrete orthogonal wavelets in l²(Z); both the interpolating property and the symmetric property are incompatible with the finite length less than-for discrete orthogonal wavelets in l²(Z_N). The results show the necessity to study discrete biorthogonal wavelets.