The fully developed flows in rectangular ducts are well studied for different electric conductivities of the walls ([1]), but under "no slip" condition on the duct walls. In [2] three classic MHD problems are revisited on assuming a hydrodynamic slip condition at the interface between the electrically conducting fluid and the insulating walls. One of the problems studied analytically in [2] is the problem on a fully developed ow in the rectangular duct with insulating walls and slip conditions on the Hartmann walls (the walls perpendicular to the magnetic field). We present the analytical solution to the problem on a fully developed ow of a conducting fluid in the rectangular duct with the perfectly conducting Hartmann walls and non-conducting side walls (the walls parallel to the external magnetic field) with the slip boundary condition on the side walls. The slip condition is given by the 3rd kind boundary condition ([2]).