By treating the reflection coefficients as independent variables, a new recursive algorithm is introduced which results in a lower prediction error and stable filters. Its performance is evaluated using sine waves in noise and pulse Doppler radar data, and is found to be substantially better than those of Burg's algorithm, Makhoul's covariance-lattice method and Marple's least-squares algorithm. Thus, although a lower error is not always desirable, the above procedure leads to better spectra for the type of data used. The spectrum of the new algorithm is the same as that of Fougere's algorithm whenever the latter reaches a solution, but its speed is substantially higher and it avoids ‘oscillations’, which made the previous computational requirements excessive. The higher speed is mainly achieved by using the covariance instead of the data in the iterations, and the ‘oscillations’ are avoided by introducing a relaxation procedure. A regular structure of VLSI implementation is also introduced.