The refined similarity hypothesis proposed by Kolmogorov in 1962 to ex
plain the intermittent structure of isotropic turbulence is modified.
It is shown that a slight but fundamental deviation from the hypothesi
s leads to success in precisely bridging between the statistics of lon
gitudinal velocity increment across distance r and that of energy diss
ipation rate averaged over a domain of scale r in a wide range of r re
aching the dissipation range, when one assumes a binomial Canter set m
odel for the latter statistics. The success also covers a reasonable p
rediction of the statistics of longitudinal velocity gradient with pro
per skewness and kurtosis for any large Reynolds number based on the T
aylor microscale.