The difference Schrӧdinger equation ψ(z+h)+ψ(z−h)+v(z)ψ(z) = Eψ(z), z ∈ ℂ, is considered, where h > 0 and E ∈ ℂ are parameters and v is a function analytic in a bounded domain D ⊂ ℂ. An asymptotic method is developed for studying its solutions in the domain D for small positive h.