We propose a minor extension of the Graph Store Protocol and the SPARQL syntax that should be sufficient to enable the application of rules to some kinds of RDF Streams (as defined by the the RDF Stream Processing W3C Community Group) to generate new RDF streams. The IRI identifying an RDF stream is extended with a query string field-value pair defining a sequence of windows of the stream. The extended IRI is passed to a data concentrator, which recasts the stream as a dynamic RDF dataset. A SPARQL query may then be applied to this dynamic dataset whenever it is updated, i.e. when the content of the next window as been fully received. The SPARQL query uses the CONSTRUCT form to generate a new element of the resultant RDF stream. The approach is illustrated with a prototypical example from the healthcare domain.