The epitaxial growth of a Bi2Sr2CuO6 (2201) thin film on a Bi2Sr2CaCu2O8 (2212) single crystal has been performed using computer-controlled laser molecular beam epitaxy. The surface of the 2212 single crystal used as the substrate is smooth and invariant under the growth condition at 640-degrees-C in NO2 pressure of 1 x 10(-5) mbar. The growth process of the 2201 film has been observed by in situ reflection high-energy electron diffraction (RHEED), and the layer-by-layer growth of the 2201 phase is confirmed by the oscillation of RHEED intensities. During the growth, a modulated surface structure which is characteristic of the Bi cuprate crystals is always present.