A new method is proposed to estimate the direction‐of‐arrivals (DOAs) of multiple narrow‐band signals using a co‐prime array (CPA). The CPA is divided into two uniform linear arrays (ULAs) and two polynomials are derived by utilising the unitary transformation technique on the covariance matrices of these two ULAs. Rather than rooting the two polynomials straightforwardly, their first‐order derivatives are exploited to construct a new difference polynomial, and DOAs are uniquely estimated without ambiguity by finding the roots of this difference polynomial that lie closest to the unit circle. The new technique shows improved accuracy with reduced complexity as compared to most state‐of‐the‐art methods, which are verified by numerical simulations.