  Recently a high-precision measurement of the Lamb shift in muonic hydrogen
has been performed. An accurate value of the proton charge radius can be
extracted from this datum with a high accuracy. To do that a sufficient
accuracy should be achieved also on the theoretical side, including an
appropriate treatment of higher-order proton-structure effects. Here we
consider a higher-order contribution of the finite size of the proton to the
Lamb shift in muonic hydrogen. Only model-dependent results for this correction
have been known up to date. Meantime, the involved models are not consistent
either with the existing experimental data on the electron-proton scattering or
with the value for the electric charge radius of the proton extracted from the
Lamb shift in muonic hydrogen. We consider the higher-order contribution of the
proton finite size in a model-independent way and eventually derive a
self-consistent value of the electric radius of the proton. The re-evaluated
value of the proton charge radius is found to be R_E=0.84022(56) fm.
