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In this paper we present new edge splitting-off results maintaining all-pairs edge-connectivities of a graph. We first give an alternate proof of Mader's theorem, and use it to obtain a deterministic $\tilde{O}({r_{\max}}^2 \cdot n^2)$-time complete edge splitting-off algorithm for unweighted graphs, where r max denotes the maximum edge-connectivity requirement. This improves upon the best known algorithm by Gabow by a factor of $\tilde{\Omega}(n)$. We then prove a new structural property, and use it to further speedup the algorithm to obtain a randomized $\tilde{O}(m + {r_{\max}}^3 \cdot n)$-time algorithm. These edge splitting-off algorithms can be used directly to speedup various graph algorithms.