In this paper Riemannian manifolds with a harmonic Weyl’s tensor are investigated. The class of these manifolds contains: Einstein’s manifolds, the results of Einstein’s manifolds products, conformally flat Riemannian manifolds. Generally, the problem of a classification of Riemannian manifolds with a harmonious Weyl’s tensor is considered rather difficult. Naturally therefore to consider it in a class of homogeneous Riemannian spaces, and in particular in a class of Lie groups with a left invariant Riemannian metrics. In dimension three Weyl’s tensor is trivial. Therefore there is a question of a harmony of the Weyl’s tensor on metric Lie groups of dimension more than three. Four-dimensional unimodular Lie algebras of Lie groups with a left invariant Riemannian metrics and a harmonious Weyl’s tensor were studied by authors. This paper continues these researches in nonunimodular case. In this paper four-dimensional nonunimodular decomposable Lie groups with a left invariant Riemannian metrics, and a harmonious Weyl’s tensor are investigated. Some methods which allow to reduce this problem to the decision of the system of the polynomial equations in Lie algebras are obtained. Full classification of four-dimensional nonunimodular decomposable Lie groups with a left invariant Riemannian metrics, and harmonious Weyl’s tensor is obtained with the help of the methods of differential geometry, mathematical analysis and computer algebra. As a result of this classification the Lie algebras with metric Lie groups which aren’t conformally flat, i.e. have non trivial Weyl’s tensor are distinguished.