This paper presents a new class of Tchebichef moments in polar coordinate form, using which rotational invariants can be easily constructed. The structure of the invariants is very similar to that of Zernike and Pseudo-Zernike moments, and their computation does not involve discrete approximation of continuous integral terms. The invariants are thus very robust in the presence of image noise, and have far better recognition capabilities when compared with Zernike/Legendre moments. The new class of moment invariants presented in this paper can be used in pattern and character recognition tasks.