In this paper, we obtain a non-asymptotic bound for Gaussian approximations for centered high-dimensional non-degenerate U-statistics over the class of hyperrectangles via exchangeable pairs and Stein's method. We improve the upper bound of the convergence rate from n in Chen (2018) to n up to a polynomial factor of logd under the same conditions, where n is the sample size and d is the dimension of the U-statistic. Convergence to zero of the bound requires logd=o(n) in Chen (2018), this requirement on d is weaken in this paper by allowing logd=o(n).