  We present a condition in which the dimer-monomer state is exactly the ground
state of an extended diamond chain with spin magnitude 1/2. The Hamiltonian of
the extended diamond chain includes next-nearest-neighbor exchange interactions
and distortions, where the spin magnitude of the spin pair on a singlet dimer
is not generally conserved. The method of deriving the condition is based on
representing the Hamiltonian in a complete square form. The dimer-monomer
ground state is found even if the Hamiltonian has no space-reflection
symmetries.
