Packet classification on multiple header fields is one of the basic techniques used in network devices such as routers and firewalls, and usually the most computation intensive task among others. To determine what action needs to be taken to a packet, a network device responsible for packet classification must identify the packet's property, such as associated packet flow, based on multiple fields of its header. Fast packet classification on multiple fields is known to be difficult mathematically and expensive practically. In this paper, we describe and discuss a fast packet classification algorithm using a multiple stage reduction scheme similar to the previously well-known recursive flow classification (RFC) algorithm. The proposed hierarchical space mapping (HSM) algorithm requires much less memory usage than RFC while keeps average search time on the same order. HSM has been proved to be very effective with commercial products in real networks.