The paper presents a new approach to the design of a uniform linear array with partial adaptivity. The technique uses the symmetric and skew-symmetric eigenvectors of a certain symmetric Toeplitz matrix to form the fixed weighting vector for the main beam and the transformation matrix for the cancellation beam. This approach allows the adaptive dimension of the processor to be reduced to about half of that of the full processor without prior knowledge of the interference field. Eigendecomposition is performed on matrices of dimensions that are half that of the number of elements. Numerical results show that the new approach is effective in designing partially adaptive uniform linear arrays.