Channel estimation is the main hurdle to reaping the benefits promised by the intelligent reflecting surface (IRS), due to its absence of ability to transmit/receive pilot signals as well as the huge number of channel coefficients associated with its reflecting elements. Recently, a breakthrough was made in reducing the channel estimation overhead by revealing that the IRS-BS (base station) channels are common in the cascaded user-IRS-BS channels of all the users, and if the cascaded channel of one typical user is estimated, the other users' cascaded channels can be estimated very quickly based on their correlation with the typical user's channel . One limitation of this strategy, however, is the waste of user energy, because many users need to keep silent when the typical user's channel is estimated. In this paper, we reveal another correlation hidden in the cascaded user-IRS-BS channels by observing that the user-IRS channel is common in all the cascaded channels from users to each BS antenna as well. Building upon this finding, we propose a novel two-phase channel estimation protocol in the uplink communication. Specifically, in Phase I, the correlation coefficients between the channels of a typical BS antenna and those of the other antennas are estimated; while in Phase II, the cascaded channel of the typical antenna is estimated. In particular, all the users can transmit throughput Phase I and Phase II. Under this strategy, it is theoretically shown that the minimum number of time instants required for perfect channel estimation is the same as that of the aforementioned strategy in the ideal case without BS noise. Then, in the case with BS noise, we show by simulation that the channel estimation error of our proposed scheme is significantly reduced thanks to the full exploitation of the user energy.