We report results of a series of high-resolution direct numerical simulations (DNSs) of forced incompressible isotropic turbulence with the number of grid points and the Taylor scale Reynolds number Rλ up to 122883 and ∼2250, respectively. The DNSs show that there exists a scaling range (approximately 100<r/η<400), at which the second-order two-point velocity structure functions S2(r) fit well with a simple power-law, S2(r)/(ϵr)2/3=C2(r/L0)ζ, where r is the distance between the two points, η is the Kolmogorov length scale, ϵ is the mean rate of energy dissipation per unit mass, and L0 is the integral length scale. The exponent ζ is constant independent from Rλ. However, the coefficient C2 is dependent of Rλ or the viscosity. This implies that the power-law scaling range of 100<r/η<400 for Rλ up to ∼2250 is not the so-called "inertial subrange"in the sense that the statistics in the range are independent from the viscosity, as assumed in various turbulence theories. This suggests that the constancy of the scaling exponent of a structure function within a certain range does not necessarily mean that the exponent is the scaling exponent in "the inertial subrange."