By Langlands [13], and Deligne [4] we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field F of characteristic zero, we have to compute the lambda function λK/F for a finite extension K/F. In this paper, when a finite extension K/F is Galois, we give a formula for λK/F.