This paper examines the privatization policy of an upstream state-owned enterprise (SOE) that competes with a foreign private rival and a downstream SOE, wherein the upstream firm supplies an intermediate input to the downstream firms. Specifically, the study investigates two scenarios where the intermediate input is utilized in either the traded or non-traded sector. In the traded sector, foreign competition exists, while the non-traded sector consists of all domestic firms. The findings of the study indicate that, in the model where the downstream is a traded sector, partial privatization of the upstream SOE is not optimal when the downstream SOE is fully nationalized or privatized. On the other hand, in the model where the downstream is a non-traded sector, partial privatization of the upstream SOE is optimal when the downstream SOE is fully nationalized or fully privatized. Therefore, the study suggests that if the upstream industry supplies its product mainly to the non-traded sector, such as domestic transportation or construction, partial privatization of the upstream SOE is recommended. However, if the intermediate input primarily flows to traded sectors, such as steel or international shipment, partial privatization of the upstream SOE is not advisable.