There is growing interest in the area of general type-2 fuzzy systems, with a increasing number of representations and approaches emerging which attempts to achieve the perceived benefits of type-2 systems without requiring the prohibitive level of computational expense. This paper presents a new recursive procedure for calculating the centroid of a general type-2 fuzzy set as given by the extension principle in an efficient way. The results given here demonstrate that this new recursive defuzzifier will be of great interest to researchers working on defuzzication algorithms for general type-2 fuzzy sets and show potential for real world application.