In this thesis, a formalism for studying the anisotropic interaction between two substitutional magnetic impurities and the magnetic anisotropic effect in a dilute noble metal-transition metal magnetic alloy has been developed from relativistic scattering theory. The theoretical development and the computational techniques of this formalism are based on relativistic spin-polarised scattering theory and relativistic band structure frameworks. For studying the magnetic anisotropic effect a convenient ‘working’ frame of reference with its axes oriented along the fee crystal axes is set up. This formalism is applied to study the situation for two Fe impurities in both paramagnetic Au (heavy) and Cu hosts. For AuFe dilute alloy, the two impurity site interaction as a function of separation is not oscillatory and the anisotropic effect is found to be less than the two site interaction itself only by an order of magnitude. Apart from the anisotropic coupling of the two impurity spins to the separation vector, for the first time, another weak anisotropic coupling to the crystal axes is also contained in the two site interaction. These anisotropic effects are the results of the relativistic spin-orbit interaction which are incorporated into the formalism.