Thin films of terbium-cobalt alloy have been deposited by magnetron sputtering. They exhibit an out-of-plane magnetic anisotropy that may result in elongated domains. The effect of thicknesses and compositions on the domain structure has been studied systematically. The composition and thickness of the films have been verified by Rutherford backscattering spectrometry and x-ray reflectivity. The domain structure was imaged by magnetic force microscopy and hysteresis loops were measured by MOKE (Magneto-optical Kerr effect). Very long and contrasted domains are obtained on the as-grown film with a thickness of 290 Å containing 8.1\% of terbium. Similar very elongated domains are obtained for other thicknesses and compositions if the films are demagnetized.