The 20 → 3−1 E-type transition of 13CH3OH at 14.78 GHz has been detected towards four continuum sources: Sgr B2, two positions in Sgr A (the peaks of the ' + 20 km/s' and the '40 km/s' clouds), and W33. The NASA Deep Space Network 70-m antenna near Canberra, Australia, which has a 66 arcsec beam at this frequency, was used. A comparison of the 13C and 12C profiles for Sgr B2 indicates a rest frequency of 14,782.27 ± .03 MHz, 0.12 MHz above the laboratory value of Haque et al. (1974). For the Galactic Centre sources, the 12C/13C abundance ratios derived using the simplest assumptions lie in the range 30–40, higher than the 20–25 range derived from H2CO observations. For W33 the apparent value of ∼ 50 is lower than the value of ∼100 derived by Henkel et al. (1983) from H2CO. There may be no discrepancy, however, as W33 contains two velocity components — the higher velocity one at 36 km/s is more prominent in CH3OH and the lower 33 km/s more prominent in H2CO.