We investigate a discontinuous boundary value problem which consists of a Sturm-Liouville equation with piecewise continuous potential together with eigenparameter dependent boundary conditions and supplementary transmission conditions. We establish some spectral properties of the considered problem. In particular, it is shown that the problem under consideration has precisely denumerable many eigenvalues λ1, λ2, ...,which are real and tends to +∞. Moreover, it is proven that the generalized eigenvectors form a Riesz basis of the adequate Hilbert space