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We propose a new parallel Branch and Bound algorithm for the Quadratic Assignment Problem, which is a Combinatorial Optimization problem known to be very hard to solve exactly. An original method to distribute work to processors using the notion of Feeding Tree is presented. When adequately used, it allows to reduce memory contention and load unbalance. Therefore, a linear speed-up in the number of processors is reached on a shared memory multiprocessor, the Cray 2 and the optimality of solutions for famous problems of size less than 20 (Nugent 16, Elshafei 19, Scriabin-Vergin 20,…) is proved by this program. The implementation analysis shows that these results are more than an improvement due to hardware evolution and confirms the usefulness of our parallel Branch and Bound algorithm for larger Quadratic Assignment Problems.