  The formation of Stationary Localized states due to a nonlinear dimeric
impurity embedded in a perfect 1-d chain is studied here using the appropriate
Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity
has the form, $\chi |C|^\sigma$ where $C$ is the complex amplitude. A proper
ansatz for the Localized state is introduced in the appropriate Hamiltonian of
the system to obtain the reduced effective Hamiltonian. The Hamiltonian
contains a parameter, $\beta = \phi_1/\phi_0$ which is the ratio of stationary
amplitudes at impurity sites. Relevant equations for Localized states are
obtained from the fixed point of the reduced dynamical system. $|\beta|$ = 1 is
always a permissible solution. We also find solutions for which $|\beta| \ne
1$. Complete phase diagram in the $(\chi, \sigma)$ plane comprising of both
cases is discussed. Several critical lines separating various regions are
found. Maximum number of Localized states is found to be six. Furthermore, the
phase diagram continuously extrapolates from one region to the other. The
importance of our results in relation to solitonic solutions in a fully
nonlinear system is discussed.
