Let G be a real semi-simple Lie group, connected, with finite centre, and K a maximal compact subgroup of G. The author considers multipliers of the convolution algebra \({\mathcal D}(G)_{(K)}\) of smooth, compactly supported functions on G, which are left and right K-finite. Let \({\mathfrak a}\) be a Cartan subspace defined by the Lie algebra of a maximally split \(\Theta\)-stable Cartan subgroup of G. Let \(W_ C\) the Weyl group which acts on \({\mathfrak a}\). \({\mathcal E}'({\mathfrak a})^{W_ C}\) denotes compactly supported, \(W_ C\)-invariant distributions on \({\mathfrak a}\). The author gives a homomorphism from \({\mathcal E}'({\mathfrak a})^{W_ C}\) into the algebra of multipliers of \({\mathcal D}(G)_{(K)}\). This was proved first by \textit{J. Arthur} [Acta Math. 150, 1-89 (1983; Zbl 0514.22006)]. However the construction of multipliers for \({\mathcal D}(G)_{(K)}\) in this paper is very simple and elementary.