In order to calculate the cyclotron radiation of a plane boundary between a non-relativistic field-free maxwellian plasma and a homogeneous vacuum magnetic field, it is first necessary to ascertain the transition function. While the general solution of this problem is not yet known, H. Grad has given a solution for a collisionless plasma neglecting the electric field between electrons and ions. A numerical evaluation of Grad's formula is given in this paper.Based on this result, the cyclotron radiation of an electron impinging on the boundary is calculated. The total cyclotron radiation of a unit area of the boundary is found to be proportional to the 3/2 power of the density and to the square of the temperature. If magnetic field is excluded from a plasma, except for the thinnest possible transition layer, it is found by comparison with bremsstrahlung that cyclotron radiation losses of a magnetically confined plasma are negligible except for an extremely high temperature, low density plasma.