The paper is concerned with the time efficient processing of spatiotemporal predicates, i.e. spatial predicates associated with an exact temporal constraint. A set of such predicates forms a buffer query or a Spatio-temporal Pattern (STP) Query with time. In the more general case of an STP query, the temporal dimension is introduced via the relative order of the spatial predicates (STP queries with order). Therefore, the efficient processing of a spatiotemporal predicate is crucial for the efficient implementation of more complex queries of practical interest. We propose an extension of a known approach, suitable for processing spatial predicates, which has been used for the efficient manipulation of STP queries with order. The extended method is supported by efficient indexing structures. We also provide experimental results that show the efficiency of the technique.