The window access schemes for input-buffered ATM switching fabrics are studied. The maximum switch throughput with a traditional Dependent Window Access (DWA) scheme is analyzed; an Independent Window Access (IWA) scheme is proposed, and the performances of an input-buffered ATM switching fabric with the IWA scheme, including the average cell delay and the maximum throughput, are analyzed by means of a probability generating functions approach. The analytical results show that the IWA scheme makes the switching fabric have better performances than the DWA scheme, and improvements of the performance are more significant for smaller windows size. Finally, the accuracy of the calculated results is verified by computer simulations.