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Broadcasting which is a primitive communication problem is to distribute the same message from a source node to all other nodes. The topology considered in this paper is the WK-recursive network that demonstrates many attractive properties, such as high degree of regularity, symmetry and efficient communication. Particularly, for any specified number of degree, it can be expanded to arbitrary size level without reconfiguring the links. A stack-base broadcasting algorithm has been proposed for WK-recursive networks. To perform this algorithm, a stack of O(log N), where N is the number of nodes, to keep the labels of links is included in each message. Moreover, when a node receives a message, a series of pop and push operations on this stack of O(log N) time complexity are required. In this paper, we present a novel broadcasting scheme for WK-recursive networks, which is much simpler and requires only constant data included in each message and constant time to determine the neighbors to forward the message.