It is believed that relativistic jets from several kinds of objects in the universe are all formed by violent phenomena near the black holes. Among the proposed mechanisms, the magnetic mechanism of the jet formation becomes most promising because it may explain not only the acceleration but also the collimation of the jets. However, the distinct mechanism has not yet been shown. Here we report numerical results of jet formation driven by magnetic field due to the current loop near a rapidly rotating black hole, based on the general relativistic magnetohydrodynamics (GRMHD). In such magnetic configuration, there are magnetic flux tubes which bridge the region between the ergosphere and the disk around the black hole. We call the magnetic flux tubes `magnetic bridges’. The result clearly shows that the `magnetic bridges\/ between the ergosphere and the disk are not stationary and expand explosively to form a relativistic jet. Furthermore, it suggests that the magnetic reconnection is caused in the expanding magnetic bridges frequently. To study the magnetic reconnection near the black hole, we have to take account of the electric resistivity. The basic method, tests, and the applications of the GRMHD with resistivity are shown.