  We compute the anomalous dimension of the second moment of the transversity
operator, \bar{\psi} \sigma^{\mu\nu} D^\rho \psi, at three loops in both the
MSbar and RI' schemes. As a check on the result we also determine the O(1/N_f)
critical exponent of the n-th moment of the transversity operator in
d-dimensions in the large N_f expansion and determine leading order information
on the n dependence of the anomalous dimension at three and four loops in
MSbar. In addition the RI' anomalous dimension of the non-singlet twist-2
operator, \bar{\psi} \gamma^\mu D^\nu \psi, is also determined.
