An efficient rotation pattern is presented that can be used in the construction of a band matrix from spectral data. The procedure allows for the stable O (n-sq) construction of a real symmetric band matrix having specified eigenvalues and first p components of its normalized eigenvectors. The procedure can also be used in the second phase of the construction of a band matrix from the interlacing eigenvalues. Previously presented algorithms for these reductions using elementary orthogonal similarity transformations require O (n- cubed) arithmetic operations. Keywords: Band matrix, Inverse eigenvalue problem, Givens rotations. (jhd