  Based on the systematic investigation of the data available for $A \geq 40$,
a $Z^{1/3}$ dependence for the nuclear charge radii is shown to be superior to
the generally accepted $A^{1/3}$ law. A delicate scattering of data around
$R_c/Z^{1/3}$ is infered as owing to the isospin effect and a linear dependence
of $R_c/Z^{1/3}$ on $N/Z$ (or $(N-Z)/2$) is found. This inference is well
supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB)
calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes
including the exotic nuclei close to the neutron drip line. With the linear
isospin dependence provided by the data and RCHB theory, a new isospin
dependent $Z^{1/3}$ formula for the nuclear charge radii is proposed.
