In this paper, we propose a direction-of-arrival (DOA) estimation method by combining multiple signal classification (MUSIC) of two decomposed linear arrays for the corresponding coprime array signal processing. The title “DECOM” means that, first, the nonlinear coprime array needs to be DECOMposed into two linear arrays, and second, Doa Estimation is obtained by COmbining the MUSIC results of the linear arrays, where the existence and uniqueness of the solution are proved. To reduce the computational complexity of DECOM, we design a two-phase adaptive spectrum search scheme, which includes a coarse spectrum search phase and then a fine spectrum search phase. Extensive simulations have been conducted and the results show that the DECOM can achieve accurate DOA estimation under different SNR conditions.