The maximum entropy method (MEM) suggested by Burg is claimed to give power spectral estimates with high resolution, especially for short records. However, we can produce examples for which Burg's algorithm gives unrealistic spectra. It is shown that the algorithm fails when applied to minimum phase wavelets. A new algorithm, one-sided Burg algorithm, is proposed to circumvent this difficulty. Both the new and original algorithms give reasonable spectral estimates when they are applied to stationary data.