This paper proposes a novel design method of two-dimensional (2-D) non-separable linear-phase paraunitary filter banks (LPPUFB). The two-degree vanishing moment constraint is derived for the lattice structure. In the 2 x 2-decomposition case, the authors have already derived the constraint and designed non-separable symmetric orthonormal wavelets with two-degree vanishing moments. This work extends the discussion to more general 2m(y) x 2m(x)-decomposition case and yields a method to impose the condition to the lattice structure. The constraint is imposed directly on design parameters so that both of the linear-phase and paraunitary property are structurally guaranteed. It is shown that the two-degree vanishing moment constraint reduces the number of parameters to be freely chosen and gives a smooth lowpass filter. Several design examples are shown to verify the significance of the novel constraint on the lattice structure.