<p>Direction of arrival (DOA) or angle of arrival (AOA) extraction is an important task in electronic warfare, communication, and radar applications. Most existing methods suffer from a high computational burden, thus making them unsuitable for practical hardware implementations. In many practical applications, there is a trade-off between limited computational resources, power usage, and accuracy. In this paper, through introducing and developing the bordered-trace-vector and utilizing the flipped-Toeplitz covariance matrix, a simple method is introduced for DOA extraction in a uniform linear array (ULA) structure. Initially, array steering vector, covariance matrix, and correlation vector are computed. Next, Toeplitz matrix is created by correlation vector. Thereafter, by flipping the Toeplitz matrix, the spectrum is modified. Then, the trace is calculated and saved in the Trace vector. Subsequently, through bordering mechanism, the dimensions of Toeplitz matrix are enhanced and the process is repeated for a specific number of times. Finally, by employing projection mechanism on the Trace vector, the angles are derived. The proposed method offers low computational burden, while also bearing some constraints in spatial coverage and resolution. It could be for rough warning scenarios with medium to high SNR, low resolution requirements, and ambiguity regarding negative angles. As a by-product of this paper, the Final-Trace theorem is introduced and proved which could be employed for joint DOA-frequency extraction in a single platform.</p>