We propose a two dimensional (2D) direction of arrival (DOA) estimation algorithm with multiple signals incident on an L-shaped array. The classical root-MUltiple SIgnal Classification (MUSIC) algorithm for an L-shaped array requires the solution of a 2D polynomial equation, a step that imposes high computational complexity. We propose a method to estimate the DOA of the incident signals using the traditional one-dimensional (1D) MUSIC in each arm of the L-shaped array; the key contribution here is an efficient and effective algorithm to pair the estimates in each arm. The pairing is based on finding the local maxima of the 2D MUSIC statistic over the possible estimated frequencies obtained by the two 1D MUSIC processes. Finally, we derive the Cramer-Rao Bound (CRB) for the estimation of the paired frequencies in the general case of colored noise. The simulation results compare the performance of the proposed method in comparison with available methods and the CRB.