Previous work showed that vehicle attitude propagation accuracy for a slewing angular rate vector can be greatly improved by including the slew rate of the angular rate vector in the propagation algorithm. The improved algorithm employs two sequential rotational increments for each time step. This work presents a method to combine the two rotational increments into a single rotational increment driven by a Universal Angular Rate vector. The Universal Angular Rate vector can be used in the direction cosine and quaternion attitude propagation algorithms to obtain attitude propagation accuracy equivalent to the two rotational increment method. An approximate Universal Angular Rate vector was also derived that avoids the use of trigonometric functions while retaining very high attitude propagation accuracy. Pure coning motion was used to stress test the Universal Angular Rate vector and the approximate Universal Angular Rate vector using direction cosine, linear direction cosine, quaternion, and Bortz propagation algorithms. Results confirmed that by replacing the standard angular rate vector with the Universal Angular Rate vector, attitude propagation accuracy is greatly improved.