  The nonlinear Maxwell Lagrangian preserving both conformal and SO(2)
duality-rotation invariance has been introduced very recently. Here, in the
context of Einstein's theory of gravity minimally coupled with this nonlinear
electrodynamics, we obtain a black hole solution which is the
Reissner-Nordstr\"{o}m black hole with one additional parameter that is coming
from the nonlinear theory. We employ the causality and unitarity principles to
identify an upper bound for this free parameter. The effects of this parameter
on the physical properties of the black hole solution are investigated.
