  We disclose a novel phase transition in black hole physics by investigating
thermodynamics of charged dilaton black holes in an extended phase space where
the charge of the black hole is regarded as a fixed quantity. Along with the
usual critical (second-order) as well as the first-order phase transitions in
charged black holes, we find that a finite jump in Gibbs free energy is
generated by dilaton-electromagnetic coupling constant, $\alpha$, for a certain
range of pressure. This novel behavior indicates a small/large black hole
\emph{zeroth-order} phase transition in which the response functions of black
holes thermodynamics diverge e.g. isothermal compressibility. Such zeroth-order
transition separates the usual critical point and the standard first-order
transition curve. We show that increasing the dilaton parameter($\alpha$)
increases the zeroth-order portion of the transition curve. Additionally, we
find that the second-order (critical) phase transition exponents are unaffected
by the dilaton parameter, however, the condition of positive critical
temperature puts an upper bound on the dilaton parameter ($\alpha<1$).
