In this paper, finite-time attitude consensus control laws for multi-agent rigid body systems are presented using rotation matrices. The control objective is to stabilize the relative configurations in a finite convergence time. First, the control design is done on the kinematic level where the angular velocities are the control signals. Next, the design is conducted on the dynamic level in the framework of the tangent bundle TSO(3) associated with SO(3), where the torques implement the feedback control of relative attitudes and angular velocities. The Lyapunov-based almost global finite-time stability of the consensus subspace is demonstrated for both cases. Finally, numerical simulations are provided to verify the effectiveness of the proposed consensus control algorithms.