In this paper, we present a new worst-case response time analysis technique for transactions scheduled by fixed priorities. In the general context of tasks with offsets (general transactions), only exponentialmethods are known to calculate the exact worst-case response time of a task. The known pseudopolynomial techniques give an upper bound of the worst-case response time. The new analysis technique presented in this article gives a better (i.e. lower) pseudo-polynomial upper bound of worst-case response time. The main idea of this approach is to combine the principle of exact calculation and the principle of approximation calculation, in order to decrease the pessimism of Worst-case response time analysis, thus allowing to improve the upper bound of the response time provided while preserving a pseudo-polynomial complexity.