Several periods close to 0.5 d have been reported for μ Cen. We obtained over 300 echelle spectra and simultaneous multicolour photometry over a two-week period. We find that the period is 0.66 d and is, in fact, singly periodic. Greyscale images of many consecutive nights show moving features which do not repeat nightly, as may be expected for P = 0.5 d, but repeat approximately every alternate night. In spite of this, periodogram analysis of the radial velocity, as measured at the point of minimum intensity in the spectral line, does indeed show a 0.5-d period. The amplitude of this periodicity decreases during the course of the run. This seeming contradiction, as well as the apparent multiperiodicity, is due to the use of period finding techniques which exclude singly-periodic solutions of a complex nature. We interpret the variations as due to two, co-rotating, circumstellar clouds distributed around the star, such that they are separated by a time interval of 0.5 d. It appears that μ Cen is another example of the growing list of Be stars in which the periodicity is due to co-rotating photospheric clouds.