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There are many existing clustering protocols that aim at making the sensor network stay functioning longer out of which Low-Energy Adaptive Clustering Hierarchy (LEACH) and Threshold-based LEACH (T-LEACH) protocols. T-LEACH protocol takes advantage of LEACH main deficiency, which is about having high control overhead. In other words, T-LEACH proposes that cluster heads do not have to turn over every round but rather every batch of rounds. Nodes will keep serving as cluster heads as long as their energy is higher than a threshold energy. This article imposes upon major drawbacks of T-LEACH and proposes a Modified Threshold-based Cluster Head Replacement (MT-CHR). In MT-CHR, a new probability of being a cluster head, for any node in any round, has been proposed which agrees fairly with the assumptions introduced in LEACH protocol.