The structural phase transitions of free-standing thin films of N-(4-n-butyloxybenzylidene)-4-n-octylaniline (4O.8), which exhibits smectic-A and crystal-B phases in the bulk, have been studied in detail using electron diffraction. When a smectic-A film is cooled, the outermost layer transforms initially to the hexatic-B phase and subsequently to the crystal-B phase at a lower temperature. The first transition is consistent with the thermal anomaly in the heat capacity and the second transition coincides with the shear response observed in mechanical measurements. Upon further cooling, the film undergoes additional layer-by-layer smectic-A-hexatic-B-crystal-B transitions in its interior.