  Crum's theorem in one-dimensional quantum mechanics asserts the existence of
an associated Hamiltonian system for any given Hamiltonian with the complete
set of eigenvalues and eigenfunctions. The associated system is iso-spectral to
the original one except for the lowest energy state, which is deleted. A
modification due to Krein-Adler provides algebraic construction of a new
complete Hamiltonian system by deleting a finite number of energy levels. Here
we present a discrete version of the modification based on the Crum's theorem
for the `discrete' quantum mechanics developed by two of the present authors.
