We present a new fully dynamic algorithm for maintaining betweenness centrality (BC) of vertices in a directed graph G=(V,E) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized O((ν^*)^2 ^2 n) time per update, where n = |V| and ν^* bounds the number of distinct edges that lie on shortest paths through any single vertex. This result improves on the amortized bound for fully dynamic BC in [Pontecorvi-Ramachandran2015] by a

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... garithmic factor. Our algorithm uses new data structures and techniques that are extensions of the method in the fully dynamic algorithm in Thorup [Thorup2004] for APSP in graphs with unique shortest paths. For graphs with ν^* = O(n), our algorithm matches the fully dynamic APSP bound in [Thorup2004], which holds for graphs with ν^* = n-1, since it assumes unique shortest paths.