NORX is one of the fifteen candidates selected for the third round of the CAESAR (authenticated encryption:security, applicability, and robustness) competition. And its only nonlinear component is made up of XOR, AND and shift operations. The design rationale of the shift parameter of NORX from the perspective of nonlinear approximation and rotational properties were studied. On the one hand, the nonlinear approximation probability of the shift function is theoretically proved to be a three-valued function. When the shift parameter is 1, this function possesses the best nonlinear property. On the other hand, the rotational probability of the shift function is formulated. And it is proved that the maximal rotational probability is the same for all nonzero shift parameters. From the above results, the NORX has the best nonlinear approximation and rotational properties when the shift parameter takes 1. The results can be of reference to the analysis of NORX and can give theoretical guidance when designing similar ciphers.