Title: A Schwarz additive method with high order interface conditions and nonoverlapping subdomains Author: F. Nataf Abstract: The convergence of a Schwars additive method is proved for a nonoverlapping decomposition into rectangles with interface conditions of order two in the tangential direction. The whole paper is available as a compressed Postscript file by internet procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100) in the directory pub/RI/1996 under the name nataf_339.janv.ps.gz or by Xmosaic or any other www client via the CMAP www server "http://blanche.polytechnique.fr/"