Let A be a hyperplane arrangement in C-n. We prove in an elementary way that the number of decomposition factors as a perverse sheaf of the direct image Rj(*) C-(U) over tilde[n] of the constant sheaf on the complement (U) over tilde to the arrangement is given by the Poincare polynomial of the arrangement. Furthermore, we describe the decomposition factors of Rj(*) C-(U) over tilde[n] as certain local cohomology sheaves and give their multiplicity. These results are implicitly contained, with different proofs, in Looijenga [Contemp. Math., 150 (1993), pp. 205-228], Budur and Saito [Math. Ann., 347 (2010), no. 3, 545-579], Petersen [Geom. Topol., 21 (2017), no. 4, 2527-2555], and Oaku [Length and multiplicity of the local cohomology with support in a hyperplane arrangement, arXiv: 1509.01813v1].