  We propose a general method to embed target states into the middle of the
energy spectrum of a many-body Hamiltonian as its energy eigenstates. Employing
this method, we construct a translationally-invariant local Hamiltonian with no
local conserved quantities, which does not satisfy the eigenstate
thermalization hypothesis. The absence of eigenstate thermalization for target
states is analytically proved and numerically demonstrated. In addition,
numerical calculations of two concrete models also show that all the energy
eigenstates except for the target states have the property of eigenstate
thermalization, from which we argue that our models thermalize after a quench
even though they does not satisfy the eigenstate thermalization hypothesis.
