We report an episode from the Yohkoh soft X-ray observations during which antiparallel coronal magnetic fields from two separate active regions, located in opposite hemispheres, reconnect and form new transequatorial coronal loops. Strong evidence for magnetic reconnection consists of the following: (1) Transequatorial connections not previously observed are newly created, (2) an X-point and separatrix structure are clearly seen in the soft X-ray images, and (3) the plasma temperature of the downstream side of reconnection is ~4-7 MK, whereas that of the upstream side is ~2 MK. The quiet coronal plasma is significantly heated over a few days, and the overall magnetic structure of the region is completely changed as a result of magnetic reconnection. This observation suggests that magnetic reconnection occurs also in the quiet corona in a less explosive way than in solar flares and that it may contribute to the overall heating of the quiet corona.