By computing the Wilson loop expectation value {ital W}({ital C}) in the two-dimensional Schwinger model on {ital R}{sup 1}{times}{ital S}{sup 1}, we show that nonleading terms depend on the shape of the contours both on {ital R}{sup 1}{times}{ital R}{sup 1} and {ital R}{sup 1}{times}{ital S}{sup 1}. We also find that the rhombic contour and triangular contour lead to the same static potentials both on {ital R}{sup 1}{times}{ital R}{sup 1} and {ital R}{sup 1}{times}{ital S}{sup 1}. The binding energy is also affected by the choice of contour shapes on the {ital R}{sup 1}{times}{ital S}{sup 1} model. This indicates that the model on {ital R}{sup 1}{times}{ital S}{sup 1} deserves more study.