We represent the state of a circa 10-nm thick submicron dimensioned magnetic film with a superposition of two-dimensional (2D) magnetic pseudovortices. The effective intervortex exchange-stiffness potential and local magnetization angle at a complex distance z=x+iy from the kth vortex center are given by the real and imaginary parts respectively, of the function −wklnz. Each of the four corners of the rectangle has a stationary quarter vortex with negative winding (wk=−1). Two mobile semivortices with winding wk=+1 and N and S magnetic poles lie at general positions X1 and X2, respectively, along edges of the rectangle. The approximate boundary condition of vanishing M-component normal to each edge is satisfied by repeated reflections which generate a periodic extension of this vortex array to a lattice filling all of a 2D space. The internal energy V(X1,X2) is principally composed of the inter vortex exchange stiffness. Given this function, numerical evaluation of the integrated moment m=m(X1,X2) provides the functional dependence of V on m as parametrized by (X1,X2). The function V(X1,X2) has four equal minima representing states with the N and S vortices located at diagonally opposite corners, in agreement with direct numerical simulations. Therefore, the predicted hysteresis behavior of our vortex model has significantly more complex transitions than those of a uniaxial single-domain particle having only two minima. Our employment of but two variables, rather than the continuum of straightforward micromagnetics, makes possible a more insightful analysis of the smallscale structures used in storage and memory.