  For symmetric L\'evy processes, if the local times exist, the Tanaka formula
has already constructed via the techniques in the potential theory by Salminen
and Yor (2007). In this paper, we study the Tanaka formula for arbitrary
strictly stable processes with index $\alpha \in (1,2)$ including spectrally
positive and negative cases in a framework of It\^o's stochastic calculus. Our
approach to the existence of local times for such processes is different from
Bertoin (1996).
