The drawback of a conventional crossbar switch is its high complexity of switch points, O ( N 2 ), where N is the number of ports of the switch. We present an alternative design of crossbar switch (Crossbar*) which maps the locations of the switch points to a set of a finite projective plane. Since the number of points of a set of a finite projective plane is f i , the complexity of switch points is reduced to 0 ( N J N ) . We also show a simple self routing algorithm, which is essential for fast cell switching. An analytical performance evaluation for bursty traffic based on Markov Modulated Poisson Process Model (MMPP) demonstrates that the cell loss probability is about ten percent higher than that of the conventional crossbar switches due to blocking effect of the Crossbar*. 0-7803-3873-1/97 $1 0.00 0 1997 IEEE 1 84