In this paper, a general technique is proposed for solving a system of fourth-order boundary value problems. The solution is given in the form of series and its approximate solution is obtained by truncating the series. Advantages of the method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Numerical results show that the method employed in the paper is valid. Numerical evidence is presented to show the applicability and superiority of the new method.