In this paper, we investigate the tags polling problem for large, multireader RFID systems. We take an approach completely different from that used so far for multireader protocols. Up to now, in the proposed protocols for this and related problems, first readers are scheduled so that those with overlapping ranges never operate at the same time. Then, proper protocols for each so scheduled reader are applied. Here, we schedule the tags instead of the readers so that tags whose transmission can be received by a common reader, never operate at the same time. Then, we present a polling protocol that takes advantage of this paradigmatic shift. The performance improvement of our protocol over the known ones is very large, going from two times to seven times, as shown by a simulation experiment we set up, and whose results are also presented.