  A new, exact and analytical class of accelerating and charged black holes is
built, in the Einstein-Maxwell theory, thanks to the Harrison transformation.
The diagonal metric does not belong to the Petrov type D classification,
therefore it is not part of the Plebanski-Demianski spacetimes. The simplest
subcase of this family recovers the Reissner-Nordstrom black hole in the
vanishing acceleration limit and the standard C-metric in the limit of null
electric charge. More general cases can have two independent electric charges,
which can be tuned as desired, even to remain with an uncharged black hole,
such as Petrov Type I Schwarzschild, embedded in an accelerating charged
Rindler background. These accelerating black holes can be considered as a limit
of charged binary systems. Conical singularities can be possibly removed in
extremal configurations. The entropy of the conformal field theory model dual
to the extreme black hole is obtained from near horizon analysis. Magnetic,
dyonic, NUTty and Kerr-like extensions are also discussed.
