Vehicular Ad-Hoc Network (VANET) is an emerging technology which allows vehicles on the roads to communicate and exchange information with each other. Broadcast in VANET has gained a lot of attention because it is used as a building block in many VANET applications. Recently, Cell Broadcast for Streets (CB-S), a cell-based algorithm has been proposed and showed better performance compared to different classes of broadcast protocols in VANET. This paper proposes an enhancement of CB-S protocol called Efficient Broadcast for Streets (EB-S). The new efficient broadcast protocol EB-S does not use a cell-based approach as in CB-S which simplifies the implementation. It addresses CB-S limitations by selecting rebroadcast nodes as the farthest nodes within the transmission range compared to only nodes located in any other cell in CB-S. Analytical model and simulation study show that EB-S outperforms considerably the original CB-S in terms of reachability and end-to-end delay under different traffic, density, and mobility conditions.