  In this work, we consider the long-time asymptotics for the Cauchy problem of
a fourth-order dispersive nonlinear Schr\"{o}dinger equation with nonzero
boundary conditions at infinity. Firstly, in order to construct the basic
Riemann-Hilbert problem associated with nonzero boundary conditions, we
analysis direct scattering problem. Then we deform the corresponding matrix
Riemann-Hilbert problem to explicitly solving models via using the nonlinear
steepest descent method and employing the $g$-function mechanism to eliminate
the exponential growths of the jump matrices. Finally, we obtain the asymptotic
stage of modulation instability for the fourth-order dispersive nonlinear
Schr\"{o}dinger equation.
