Using temporal abstraction, various forms of sampled multivariate temporal data can be transformed into a uniform representation of symbolic time intervals, from which Time Intervals Related Patterns (TIRPs) can be then discovered. Hence, mining TIRPs from symbolic time intervals offers a comprehensive framework for heterogeneous multivariate temporal data analysis. While the field of time intervals mining has gained a growing interest in recent decades, frequent closed TIRPs mining was not investigated in its full complexity. Mining frequent closed TIRPs is highly effective due to the discovery of a compact set of frequent TIRPs, which contains the complete information of all the frequent TIRPs. However, as we demonstrate in this paper, the recent advancements made in closed TIRPs discovery are incomplete, due to the discovery of only the first instances of the TIRPs within each STIs series in the database. In this paper we introduce the TIRPClo algorithm – for complete and efficient mining of frequent closed TIRPs. The algorithm utilizes a memory-efficient index and a novel method for data projection, due to which it is the first algorithm to guarantee a complete discovery of frequent closed TIRPs. In addition, a rigorous runtime comparison of TIRPClo to state-of-the-art methods is performed, demonstrating a significant speed-up on various real-world datasets.