Second-harmonic generation (SHG) at normal incidence in transmission geometry was studied in Bi-containing magnetic garnet thin films on gadolinium-gallium garnet (GGG) substrates of (111) and (210) types. A Q-switched Nd-YAG laser was used as a radiation source. The intensity of the SHG was lower than that in crystalline quartz but it was nevertheless reliably detectable. The study of the SHG intensity as a function of the rotation angle of the films around their normals showed that the signal is well described by phenomenological expressions derived under the assumption that the point symmetry of the films is C_1h ((210) substrate) or C_3v ((111) substrate). The SHG intensity was found to be independent of temperature in the range 290-405 K, thus excluding a 'magnetic' origin of the SHG. These experiments as well as those previously published on the linear magnetoelectric effect prove that there is no inversion centre in magnetic garnet thin films.