As it’s known, The Graph k-Colorability Problem (GCP) is a wellknown NP-Hard Problem. This problem consists in finding the k minimum number of colors to paint the vertices of a graph in such a way that any two adjoined vertices, which are connected by an edge, have always different colors. In another words how can we color the edges of a graph in such a way that any two edges joined by a vertex have always different colors? In this paper we introduce a new effective algorithm for coloring the edges of the graph. Our proposed algorithm enables us to achieve a Continuously Edge Coloring (CEC) for a set of known graphs.