The problem of reflection of backward volume magnetostatic waves (BVMSWs) from a metallized portion of a ferrite film has been solved rigorously in the magnetostatic approximation. The condition of total internal reflection is formulated. This effect can be used for creation of a waveguide of BVMSWs. The waveguide is a slot in the metallic coating of a ferrite film with the slot's edges parallel to a magnetizing field. The use of such a waveguide makes it possible to avoid diffraction losses which accompany propagation of BVMSW beams in real devices. The BVMSW waveguide is convenient for connection with an active element (for example, with a Gunn diode). A simple method of calculating the dispersion characteristic of such a waveguide has been suggested. This characteristic is determined experimentally for some waveguides. The theoretical results and the experimental data are in reasonable agreement.