An analysis of fully developed turbulence is developed based on the assumpt
ion that the underlying statistics of the system is that of the Tsallis ens
emble. The multifractal spectrum f(T)(alpha) corresponding to the Tsallis-t
ype distribution function is determined self-consistently in the sense that
all parameters can be obtained through the observed value of the intermitt
ency exponent. It is shown that the scaling exponents zeta(m) of the veloci
ty structure function derived with the help of the multifractal spectrum fi
t very well with experimental data. It is revealed that the asymptotic expr
ession of zeta(m) for m much greater than 1 has a log term. The present sel
f-consistent approach narrowed down the value of intermittency exponent mu
for the fully developed turbulence to mu = 0.235 +/- 0.015.