  Additional information about the eigenvalues and eigenvectors of a physical
system demands extension of the effective Hamiltonian in use. In this work we
extend the effective Hamiltonian that describes partially a physical system so
that the new Hamiltonian comprises, in addition to the information in the old
Hamiltonian, new information, available by means of experiment or theory. A
simple expression of the enlarged Hamiltonian, which does not involve matrix
inversion, is obtained. It is also shown that the Lee-Suzuki transformation
effectively put the initial Hamiltonian in a diagonal block form.
