This paper proposes a coupling strategy that can be used for transient fluid–structure interaction. The objective of this paper is to propose a time integrator coupling strategy, which ensures good properties to couple typical solid and typical fluid time integrators in linear cases. It is evaluated on a 1-D toy problem only dedicated to the study of the quality of time integrators coupling. The structure is discretized by the linear finite element method and solved in time by the Newmark scheme, whereas the finite difference and finite volume methods are used for the fluid subdomain. By projecting the fluid equations on the eigenvector, we obtain a compatibility relation that corresponds to the characteristic line that transfers the fluid information from the inside to the fluid–structure interface. With this appropriate compatibility relation and the solid equations, the interface status is predicted for the next time step, ensuring zero interface energy. Hence, the order of accuracy and the stability are preserved to the minimum level of the two parts, the structure and the fluid. Furthermore, the coupling strategy allows incompatible time steps. Some numerical results are obtained for the 1-D linear problem, and a good agreement with the analytical solution has been found. Copyright © 2013 John Wiley & Sons, Ltd.