In this paper, we propose a novel tableaux-based algorithm for checking consistency of a $\mathcal{SHOIQ}$ knowledge base. This algorithm creates a structure consisting of a set of trees which are linked together by a partitioning function over the set of all the trees' nodes. This construction allows us to avoid building explicitly a graph with cycles and ensures that the size of created structures is exponential in size of SHOIQ knowledge bases. From this, we show that the novel algorithm is worst-case optimal for checking consistency of a SHOIQ knowledge base.