  We propose a generalization of the algebraic Bethe ansatz to obtain the
eigenvectors of the Heisenberg spin chain with general boundaries associated to
the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz
takes the usual form of a product of operators acting on a particular vector
except that the number of operators is equal to the length of the chain. We
prove this result for the chains with small length. We obtain also an off-shell
equation (i.e. satisfied without the Bethe equations) formally similar to the
ones obtained in the periodic case or with diagonal boundaries.
