Summary: This paper considers the Byzantine agreement problem in a completely connected network of anonymous processors. In this network model the processors have no identifiers and can only detect the link through which a message is delivered. We present a polynomial-time agreement algorithm that requires $3 \lfloor (n - t) t /(n - 2 t)\rfloor +4$ rounds, where $n >3 t$ is the number of processors and $t$ is the maximal number of faulty processors that the algorithm can tolerate. We also present an early-stopping variant of the algorithm.