We examine the optimal trade policy in a duopoly model where international rival firms compete in a final goods market. The domestic firm signs an OEM (Original Equipment Manufacturing) contract with and produces the final goods for the foreign firm. When the price in the OEM market is decided by the foreign firm, we prove that whether a trade pattern with the OEM contract exists depends on the comparative advantage of trading countries and on the strategic interaction between firms. We show that the domestic country should tax its exports of the OEM products, but subsidize the other exports of final goods.