The Karnik-Mendel algorithm computes the centroids of an Interval Type-2 Fuzzy Set, corresponding to the left and right endpoints of the interval centroid. According to Mendel and WU (2009), the computation of those endpoints, represent a bottleneck for interval type-2 fuzzy logic systems, and they proposed a more efficient algorithm called the Enhanced Karnik-Mendel algorithm (2009). In this paper, the monotony property of the centroids is proven, and a new algorithm is suggested based on this property and the aforementioned Enhanced Karnik-Mendel algorithm, that improves computation times when the number of rules is roughly less than 1,000.