Since Pocock (1977, Biometrika 64, 191-199), many methods have been developed for group sequential analysis of clinical trials. However, these methods remain underemployed partly because of inconsistencies of sequential testing [Berry (1987, The Statistician 36, 181-189)]. This paper considers a new approach, which, by requiring that a succession of interim analyses be significant at the alpha level, both preserves the overall significance level alpha and does not present some of the inconsistencies of the previous methods. Results are obtained for a normal or binary response and for survival data. A comparison with the usual group sequential testing is also presented.