Genetic Algorithms (GAs) are well-known heuristic algorithms and have been widely applied to solve combinatorial problems. Edge recombination is one of the famous crossovers designed for GAs to solve combinatorial problems. The essence of edge recombination is to achieve maximal inheritance from parental edges. This paper presents two strategies to improve edge recombination. First, we encourage alternation of parents in edge inheritance. Second, a greedy method is used to handle the failures occurred in edge recombination. A modified edge recombination, called edge recombination with tabu (Edge-T), is proposed according to these two strategies. The traveling salesman problem is used as a benchmark to demonstrate the effectiveness of the proposed method. Experimental results indicate that Edge-T can achieve better performance than the conventional edge recombination Edge-3 in terms of both solution quality and convergence speed.