Four ESR lines, found by Miyazaki et al. in 1995 in irradiated solid parahydrogen (ca. 92% para-purity) at 4.2 K, assigned as "H-2(-),'' were precisely re-measured with highly pure solid parahydrogen (>99.9%) and compared with calculated g-value and hyperfine coupling constants of H-2(+)(H-2)(2). The g-value of I,M-I=0,0 feature, reported previously as 2.0033 or 2.0023, was found to be incorrect and has now been corrected to 2.002120+/-0.000012. This corrected value is clearly smaller than that of free electron. We also found that the remaining three lines corresponding to I, M-I=1,0; 1, +1; and 1, -1 features have axially symmetric hyperfine anisotropic structure i.e., A(parallel to)=20.318 and A(perpendicular to)=20.502 mT. This anisotropy corresponds to the rotation of the species in solid parahydrogen. Although the experimental g-value and isotropic hyperfine coupling constants are in good agreement with those of H-2(+)(H-2)(2) estimated by ab initio calculation, it is still difficult to explain why H-2(+)(H-2)(2) clusters turned into ESR inactive species by addition of 0.1similar to1% D-2 in the present system. In this regard, we still maintain that the species in solid parahydrogen are H-2(-).