Systematic variations in the Doppler shifts of absorption lines in the spectrum of the star 51 Pegasi were interpreted as indicating the presence of a planet about half the mass of Jupiter, very close to the star(1,2). But that interpretation was called into question when variations in the line shapes that tracked the apparent orbital phase were reported(3,4); this suggested that a planet was an inadequate explanation of the radial-velocity data. Here I report results from recent monitoring of 51 Peg; the oscillations I previously published are not evident in the new data. When combined with two other high-precision observations of 51 Peg (refs 5-7), that also see no changes in line shape, a planet may indeed be the best explanation for the radial-velocity results.