According to a generic temperature vs. carrier-doping (T-p) phase diagram of high-temperature superconductors it has been proposed that as doping increases to the overdoped region they approach gradually a conventional (canonical) Fermi Liquid. However, Hall effect measurements in several systems reported by different authors show a still strong \emph{T}-dependence in overdoped samples. We report here electrical transport measurements of Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-delta} thin films presenting a temperature dependence of the Hall constant, R_H, which does not present a gradual transition towards the T-independent behavior of a canonical Fermi Liquid. Instead, the T-dependence passes by a minimum near optimal doping and then increases again in the overdoped region. We discuss the theoretical predictions from two representative Fermi Liquid models and show that they can not give a satisfactory explanation to our data. We conclude that this region of the phase diagram in YBCO, as in most HTSC, is not a canonical Fermi Liquid, therefore we call it Anomalous Fermi Liquid.