This paper proposes a revised conception of labeling algorithm, which provides a redefined way of determining a label of syntactic objects(SO). It is shown that this revised labeling algorithm gains several theoretical and empirical consequences, eliminating certain obscure complications in Chomsky's (2013, 2014) framework. We point out in the revised labeling algorithm that first, given SO={Root, XP}, minimal search which only searches the categorial feature of the head unambiguously selects the root as the label of the SO containing it. Second, given SO={XP, YP}, where the label of the SO cannot be straightforwardly determined, a feature sharing is undergone via the categorial feature of C and T. Third, given SO={NP, vP}, in order to determine the label of the SO, NP moves out of the SO in which vP can not be feature-shared with NP due to the fact the head R of vP is unspecified in the category. Thus the revised labeling algorithm that makes use of specific notions such as the root, specified/unspecified categorial features removes some unnecessary complications of Chomsky(2013, 2014) but also can give a novel answer to an unanswered question concerning CHL's phase recognition in the syntax.