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In this paper, we improve relations of the charge-radius difference of two isotopes by considering a term which relates to the proton number and the parity of the neutron number. The correction makes the root-mean-squared deviation reduce to 0.0041 fm for 651 nuclei with the neutron number larger than 20, in comparison with experimental data compiled in the CR2013 database. The improved relations are combined with the local relations consisting of charge radii of four neighboring nuclei. These combinations are also proved to be efficient in describing and predicting nuclear charge radii, and can reflect structure evolutions of nuclei. Our predictions of 2467 unknown nuclear charge radii within competitive accuracy, which are calculated by using these two kinds of relations, are tabulated in the Supplemental Material of this paper.