This technical note concerns the deterministic sampling points construction strategy for unscented Kalman filter (UKF) and cubature Kalman filter (CKF). From the numerical-integration viewpoint, a new deterministic sampling points set is derived by orthogonal transformation on the cubature points. By embedding these points into the UKF framework, a modified nonlinear filter named transformed unscented Kalman filter (TUKF) is derived. The TUKF can address the nonlocal sampling problem inherent in CKF while maintaining the virtue of numerical stability for high dimensional problems. Moreover, the methodology proposed in this technical note can be used to construct nonlinear filters with improved accuracy for certain problems. The performance of the proposed algorithm is demonstrated through a nonlinear high dimensional problem.