Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. Using the circle polynomials as the basis functions for their orthogonalization over rectangle pupil, we derive closed-form polynomials that are orthonormal over it. The polynomials are unique in that they are not only orthogonal across rectangle pupils, but also represent balanced classical aberrations, just as the Zernike circle polynomials are unique in these respects for circular pupils. The polynomials may be given in terms of the circle polynomials as well as in polar or Cartesian coordinates. Using the first 15 items of the rectangle polynomials to fit the data of interferometer of rectangle windows in the least squares method, we can get the conclusion that the first 15 items of the rectangle polynomials can be fit the data very well from the result of statistical analysis.