In this paper, stability of continuous-time Takagi- Sugeno (T-S) fuzzy systems is investigated by means of a new fuzzy Lyapunov function which depends on the first-order timederivative of the fuzzy weighting functions (TDFWF). As a result, both the first and second-order TDFWF appear in the Lyapunov inequality and the stability condition. The additional dependence on the second-order TDFWF makes it possible to reduce the conservativeness of the previous result. The stability condition is formulated in terms of linear matrix inequalities (LMIs). The effectiveness of the proposed analysis approach is demonstrated by numerical examples.