Parametric Worst-case execution time (WCET) analysis of a sequential program produces a formula that represents the worst-case execution time of the program, where parameters of the formula are user-defined parameters of the program (as loop bounds, values of inputs, or internal variables, etc). In this article we propose a novel methodology to compute the parametric WCET of a program. Unlike other algorithms in the literature, our method is not based on Integer Linear Programming (ILP). Instead, we follow an approach based on the notion of symbolic computation of WCET formulae. After explaining our methodology and proving its correctness, we present a set of experiments to compare our method against the state of the art. We show that our approach dominates other parametric analyses and produces results that are very close to those produced by non-parametric ILP-based approaches, while keeping very good computing time.