We have investigated the importance of the stratosphere-troposphere linkage on the seasonal predictability of the North Atlantic Oscillation in a pilot study using a high horizontal resolution atmospheric general circulation model, and covering the 14 winters from 1979/1980 to 1992/1993. We made an ensemble of simulations with the Meteo-France "Arpege Climat" model (V3.0) with a well-resolved stratosphere, and a broad comparison is drawn with hindcasts from previously published experiments using low-top and lower horizontal resolution models, but covering the same winters with the same ensemble size and verification method. For the January-February-March North Atlantic Oscillation index, the deterministic hindcast skill score is 0.59, using re-analyses as verification. It is comparable to the reported multi-model skill score (0.57). The largest improvement originates from the winter 1986/1987 characterised by a major stratospheric sudden warming. We demonstrate that there is then a high-latitude zonal-mean zonal wind decrease in the stratosphere-troposphere hindcasts over a broad pressure range. This is consistent with a composite analysis showing that model anomalous vortex events, either weak or strong, lead to a North Atlantic Oscillation index anomaly in the troposphere, which persists, on average, for 1 month after the anomaly peaked in the stratosphere.