Thompson  showed that the eigenvector analysis required of Pisarenko's method of harmonic retrieval can be achieved on-line without explicit eigen decomposition. His method utilizes a unit-norm constrained adaptive filter to find and track a single vector that lies in the noise subspace. By tracking this vector without explicit formulation of the sample covariance matrix R or its eigen decomposition, the algorithm maintains a low computational cost. In this paper, Thompson's method is extended using a penalty method. The new algorithm seeks an orthonormal basis that spans the noise subspace. The computational complexity of the algorithm is then reduced to a more desirable level through the use of a relaxation technique. Once the noise subspace is constructed, one can compute the MUSIC power spectrum  for an improved spectral estimate.