This paper investigates the strategic effect of bundling when a multi-product firm producing two complements faces competition in both markets. I consider a demand structure where both Cournot and Bertrand competition can be evaluated. Bundling is completely ineffective when firms compete in quantities. On the contrary, under Bertrand competition, selling the two goods in a package is profitable when the goods produced by the rivals are perceived as close substitutes to those produced by the multi-product firm. Bundling drives prices up, and not only consumer surplus, but also social welfare shrinks, thus calling for the intervention of the antitrust agency.