In the General Theory of Relativity the curvature tensor has an important role in expressing the field equations. For this purpose a certain tensor is widely used. The expression of this tensor has been derived by requiring fulfilling of three conditions. The final condition to be satisfied requires the divergence of the tensor be identically zero. Finally an expression containing two terms was obtained. After a deeper analysis of the known formula, we can see that the divergence of each of both terms is identically zero, so that instead of a single expression, we could accept infinity of expressions. This circumstance appeared because the best deductions use general formulae leading to an expression (a sum of two terms) the divergence of which is zero. The aim of the paper is to establish general expressions avoiding the mentioned situation.

Keywords: Curvature tensor, Field equations, General theory of relativity.