  We compute the area(or entropy) product formula for a regular black hole
derived by Ay\'on-Beato and Garc\'ia in 1998\cite{abg}. By explicit and exact
calculation, it is shown that the entropy product formula of two physical
horizons strictly \emph{depends} upon the ADM mass parameter that means it is
\emph{not} an universal(mass-independent) quantity. But a slightly more
complicated function of event horizon area and Cauchy horizon area is indeed a
\emph{mass-independent} quantity. We also compute other thermodynamic
properties of the said black hole. We further study the stability of such black
hole by computing the specific heat for both the horizons. It has been observed
that under certain condition the black hole possesses second order phase
transition. The pictorial diagram of the phase transition is given.
