Cover theorem is the theoretical foundation of GVW algorithm and also the core of the signature-based algorithm to eliminate a large number of useless J-pairs without any reduction. In this paper, we extend the cover theorem to the case of any semigroup order. Since a semigroup order is not necessary to be global or local, there may not be a minimal or maximal signature in an infinite set, which results in the difficulty of proving the cover theorem by the classical method. Based on the pioneering idea of Mora normal form algorithm, we propose a more essential and general proof for the cover theorem with avoiding the choice of a minimal or maximal signature. Therefore, the signature-based standard basis algorithm for any semigroup order under the framework of GVW algorithm is presented, and an example is given to illustrate the algorithm.