Due to wireless propagation condition, users in a cell experience different channel condition. Thus cell-center users have optimal condition whereas cell-edge users suffer from a severe path-loss and a low bit-rate. In this paper, a fair scheme to allocate Resource Blocks (RB) on the downlink in LTE networks is proposed. The problem addresses maximising the overall system throughput while ensuring the fair resource allocation among UEs (User Equipment). We use a new fairness criterion which is based upon the concept of the Nash Bargaining Solution (NBS) model.Our idea is to bring in a compensating factor to overcome the path-loss influence. The performance evaluation confirms that our method is able to spread resources fairly over the entire cell.