Magnetic reconnection of solar coronal loops is the main process that causes solar flares and possibly coronal heating. In the standard model, magnetic field lines break and reconnect instantaneously at places where the field mapping is discontinuous. However, another mode may operate where the magnetic field mapping is continuous but shows steep gradients: The field lines may slip across each other. Soft x-ray observations of fast bidirectional motions of coronal loops, observed by the Hinode spacecraft, support the existence of this slipping magnetic reconnection regime in the Sun's corona. This basic process should be considered when interpreting reconnection, both on the Sun and in laboratory-based plasma experiments.