Optimizing inter-vehicle distances is very important to reduce traffic congestion on highways. A modification of the constant time headway policy (CTH) has been proposed in [1]. This modification significantly reduces inter-vehicle distances, but this reduction in the inter-distance may increase the risks of collisions. In this paper, the safety of the modified CTH applied to a homogeneous platoon is addressed. Many critical scenarios are discussed, including hard braking of the leader and followers in the event of communication loss. Safety conditions are presented. In addition, a method to find the maximum allowed delay to inform all the vehicles about communication loss, is also presented. Simulations have been run with 10 vehicles to check safety in the proposed scenarios.