Stabilization of rigid body attitude motion to a desired attitude in finite time is considered here. Attitude feedback control with finite time convergence has been considered in the past using the ambiguous unit quaternion representation. However, it is known that continuous feedback control with unit quaternion feedback leads to the unstable unwinding phenomenon, which has debilitating effects on convergence of states and control effort expended. This work considers finitetime stabilization of rigid body attitude dynamics using the coordinate-free representation of attitude on the group of rigid body rotations in three-dimensional Euclidean space, SO(3). The feedback control law designed here leads to almost global finite time stabilization of the attitude motion of a rigid body with known attitude dynamics model, to the desired attitude. Almost global finite time stability of this control law is shown using a Morse function as part of a Lyapunov analysis; this Morse function has been previously used for almost global asymptotic stabilization of rigid body attitude motion.