A fully sampled and hitherto highest resolution and sensitivity observation of neutral hydrogen (H I) in the Leo Triplet (NGC 3628, M 65/NGC 3623, and M 66/NGC 3627) reveals six H I structures beyond the three galaxies. We present detailed results of the morphologies and kinematics of these structures, which can be used for future simulations. In particular, we detect a two-arm structure in the plume of NGC 3628 for the first time, which can be explained by a tidal interaction model. The optical counterpart of the plume is mainly associated with the southern arm. The connecting part (base) of the plume (directed eastward) with NGC 3628 is located at the blueshifted (western) side of NGC 3628. Two bases appear to be associated with the two arms of the plume. A clump with a reversed velocity gradient (relative to the velocity gradient of M 66) and a newly detected tail, that is to say M 66SE, is found in the southeast of M 66. We suspect that M 66SE represents gas from NGC 3628, which was captured by M 66 in the recent interaction between the two galaxies. Meanwhile gas is falling toward M 66, resulting in features previously observed in the southeastern part of M 66, such as large line widths and double peaks. An upside-down “Y”-shaped H I gas component (M 65S) is detected in the south of M 65, which suggests that M 65 may also have been involved in the interaction. We strongly encourage modern hydrodynamical simulations of this interacting group of galaxies to reveal the origin of the gaseous debris surrounding all three galaxies.