The arrowhead decomposition method which allows efficient parallel solution of a blocktridiagonal system of linear equations is presented. The computational speedup with respect to the matrix sweeping algorithm is analytically estimated by taking into account the number of elementary operations of multiplication for the parallel and serial parts of the decomposition method. It is shown that the maximal speedup is achieved for the finite number of parallel processors. For a given size of the initial system of linear equations, the parameters of the computational system which give the maximal speedup are obtained. Computational experiments confirm the analytical estimations of the computational speedup.