An edge dominating set of a graph G = (V, E) is a subset M ⊆ E of edges such that each edge in E \M is incident to at least one edge in M. In this paper, we consider the parameterized edge dominating set problem which asks us to test whether a given graph has an edge dominating set with size bounded from above by an integer k or not, and we design an O∗ (2.2351k )-time and polynomialspace algorithm. This is an improvement over the previous best time bound of O∗ (2.3147k ). We also show that a related problem: the parameterized weighted edge dominating set problem can be solved in O∗ (2.2351k ) time and polynomial space.