We present a new implementation of the second-order polarization propagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear transformation allows for more efficient calculations for large two particle-two hole excitation manifolds. Second, the operation count for SOPPA is lowered by one order, to N-5. As an application of the new implementation, we calculate the excitation energies and oscillator strengths of the lowest singlet and tripler transitions for benzene and naphthalene. The results compare well with experiment and CASPT2 values, calculated with identical basis sets and molecular geometries. This indicates that SOPPA can provide reliable values for excitation energies and response properties for relatively large molecular systems.