The exact slewing attitude transformation of a single axis that moves along a conical trajectory was derived. The result was used to increase the attitude propagation accuracy using a single axis by incorporating the slewing motion of the angular rate vector into the attitude propagation algorithm. It was shown that when the slew rate of the angular rate vector has a fixed orientation in the body frame and has a magnitude proportional to the angular rate vector magnitude, the attitude can be propagated with only numerical roundoff error. The findings not only agree with previously published results, but provide and additional new solution due to the commutative property of the associated slewing and rotational transformations. The algorithm was applied to pure coning motion having time dependent angular rate magnitude and the coning motion of axisymmetric vehicles with time dependent angular rate magnitude. Numerical examples that demonstrate the improvement in accuracy are included.