We analyze the electromagnetic field of a small bunch that uniformly moves in a circular waveguide and transverses a boundary between an area filled up with cold magnetized electron plasma and a vacuum area. The magnetic field is supposed to be strong but finite so the perturbation technique can be applied. Two cases are studied in detail: the bunch is flying out of the plasma into a vacuum, and, inversely, out of the vacuum area into the plasma. The waveguide mode components are investigated analytically with methods of the complex variable function theory. The main peculiarities of the bunch radiation in such situations are revealed.