The gamma-ray emission above 250 GeV from the BL Lac object Markarian 421 was observed by the CAT Cherenkov imaging telescope between December, 1996, and June, 2000. In 1998, the source produced a series of small flares, making it the second extragalactic source detected by CAT. The time-averaged differential spectrum has been measured from 0.3 to 5 TeV, which is well fitted with a power law with an index of -2.88+-0.12(stat)+-0.06(syst). In 2000, the source showed an unprecedented activity, with variability time-scales as short as one hour, as for instance observed during the night between 4 and 5 February. The 2000 time-averaged spectrum measured is compatible with that of 1998, but some indication of a spectral curvature is found between 0.3 and 5 TeV. The possibility of TeV spectral hardening during flares is also discussed, and the results are compared to those obtained on the other TeV BL Lac, Markarian 501. ; Comment: Latex2e, 11 pages, 7 figures, accepted for publication in Astronomy & Astrophysics