In this paper, we consider a multipoint boundary value problem for systems of integro–differential equations with an involution when the derivative of the desired function is contained in the right side of the equation. Using the properties of the involutive transformation, the problem is reduced to the study of a multipoint boundary value problem for systems of integro-differential equations. Considering an integral equation of the second kind of Fredholm type with respect to the kernel and determining its resolvent, the equation reduces to an integro-differential equation that does not contain the derivative of the desired function in the right part. Further, the parameterization method proposed by Professor D.Dzhumabaev can be applied to this problem. Based on this, the solution of the problem is reduced to solving a special Cauchy problem and a system of linear equations. Using the methods of solving integral equations, the unambiguous solvability of the original problem is reduced to the reversibility of the matrix, which depends on the initial data.