We consider a communication protocol where the sender breaks a message, comprised of an information block and a corresponding CRC, into small segments and transmits these segments separately, possibly via different routes, to the receiver. Traditionally, reversing the sender operations, the receiver first assembles all the segments that make up the message, then computes a CRC based on the information part of the message and verifies it against the arriving CRC, and, finally, delivers the information part on to the upper layer protocol (ULP). We present an incremental CRC computation whereby each arriving segment contributes its share to the message's CRC upon arrival, independently of other segment arrivals, and can thus proceed immediately to the ULP. We impose no constraint on the order of segment arrivals nor on their sizes. Yet, in its time complexity, our scheme does not exceed the traditional computation, which assembles all the segments first, and it uses only a fixed and very small amount of extra memory. Our scheme is beneficial when the ULP can process the individual segments without reading the entire message first and can revert, if needed, to the state it had prior to the processing of any segment of that message. One practical example application is the evolving protocol for remote direct memory access (RDMA) over TCP, where an overall CRC is added to a concatenation of data segments.