Deterministic approach to broadcasting in Mobile Ad Hoc Networks (MANETs) is effective in reducing redundant broadcasting. In this approach, a transmitting node selects a subset of its immediate or 1-hop neighbors to rebroadcast the message such that all its 2-hop neighbors will receive the message, or being covered. In order to reduce redundant broadcasting, the set of 1-hop neighbors to be covered should be reduced as much as possible. Another important aspect that affects the effectiveness of a deterministic broadcasting protocol is the termination condition that inhibits a node from transmitting a particular message unnecessarily. However, existing termination conditions are not optimized. We propose a new covered/uncovered termination condition where each node is assigned with covered/uncovered status. In this paper, we show that our covered/uncovered termination condition ensures full network coverage, does not incur any control message overhead, and yet requires the least number of rebroadcasting nodes. When we apply the termination condition to some existing deterministic broadcasting protocols, the saving in the number of broadcasting nodes can be as significant as 45% when there are 100 nodes randomly distributed in an area of 1000 x 1000 m 2 .