operators in various noncommutative space. Reiffel [@15] constructed the complete set of projection operators on the noncommutative torus $T^{2}$. On the basis Boca studied the projection operators on noncommutative orbifold [@16] obtaining many important results and showed the well-known example of projection operator for $T^{2}/Z_{4}$ in terms of the elliptic function. Soliton solutions in noncommutative gauge theory were introduced by Polychronakos in [@soliton]. Martinec and Moore in their important article deeply studied soliton solutions namely projectors on a wide variety of orbifolds, and the relation between physics and mathematics in this area [@11]. Gopakumar, Headrick and Spradlin have shown a rather apparent method to construct the multi-soliton solution on noncommutative integral torus with generic $\tau$[@10]. This approach can be generalized to construct the projection operators on the integral noncommutative orbifold $T^2/Z_N$ [@9].

In this paper, in the case of integral noncommutative orbifold $T^2/Z_4$ generated by $u_{1}$ and $u_{2}$ with $$u_{1}u_{2}
=u_{2}u_{1}e^{2\pi i/A},~~~A=1,2,3,\cdots$$ we generalize the $GHS$ construction, presenting the explicit symmetric form of a series of projectors with manifest $Z_{4}$ symmetry. It includes all the solutions with minimal trace, and in the standard expansions for the projectors (see equation (\[eq:41\])) $$P=\sum_{s,t}u_1^s u_2^t\Psi_{s,t}(u_1^A,u_2^A)$$ where the eigen value function $\Psi_{s,t}(v_1^A,v_2^A)$ is continuous 