Wrinkles are commonly observed in uniaxially stretched rectangular sheets with clamped-clamped boundaries, and can disappear upon excess stretching. Here we explore this wrinkling and restabilization behavior both analytically and numerically. We find that Poisson's ratio plays a crucial role in the wrinkling and restabilization behavior. Smaller Poisson's ratio makes later onset of wrinkling, lower amplitude and earlier disappearance of wrinkles. In particular, when Poisson's ratio is below a threshold, no wrinkles occur, which can be explained by the decreasing transverse compressive stresses with respect to the reducing Poisson's ratio. Furthermore, based on the Koiter stability theory, we have semi-analytically predicted isola-center bifurcation points, through looking into the sign change of the quadratic terms of potential energy. Both theoretical buckling and restabilization points are in agreement with finite element results. Lastly, a 3D phase diagram on stability boundaries is provided and we find that when the aspect ratio is beyond a threshold, wrinkles may not occur in the center but are split into two packets near the stretching ends.