We consider the problem of estimating the parameters of a real-valued, stationary, nondeterministic, autoregressive process of order p from a time series of finite length. Burg’s algorithm estimates these parameters indirectly by sequentially estimating one reflection coefficient at a time. Our approach is to sequentially eTtimate the reflection coefficients in pairs. The new algorithm has the same order of computational complexity as Burg’s. It is guaranteed to generate parameter estimates that correspond to a stationary process (as does Burg’s), and it produces estimates of the power spectral density that do not appear to suffer from spectral line splitting-in contrast to Burg’s algorithm.