In this paper, the sensitivity of Atmospheric and Oceanic Coupled Models (AOCMs) to the coupling method is investigated. We propose the adaptation of a Schwarz-like domain decomposition method to AOCMs. We show that the iterative process of the method ensures consistency of the coupled solution across the air-sea interface, contrarily to usual \textit{ad-hoc} algorithmic approaches. The latter are equivalent to only one iteration of a Schwarz-like iterative method, which does not provide a converged state. It is generally assumed that this lack of consistency does not affect significantly the physical properties of the solution. The relevancy of this statement is first assessed in a simplified problem, then in the realistic application of a mesoscale atmospheric model (WRF) coupled with a regional oceanic model (ROMS) to simulate the genesis and propagation of tropical cyclone Erica. Sensitivity tests to the coupling method are carried out in an ensemble approach.We show that with a mathematically consistent coupling the spread of the ensemble is reduced,suggesting that there is room for further improvements in the formulation of AOCMs at a mathematicaland numerical level.