An investigation of the WIMP annual modulation signature is in progress at the Gran Sasso National Laboratory of the I.N.F.N. by means of the similar or equal to 100 kg NaI(TI) DAMA set-up; the results obtained during four annual cycles have already been published. In this paper we will further address in some details the main arguments, which have allowed us to exclude known systematic effects as a possible source of the annual modulation observed in the rate at very low energy. In particular. the (more recently released) data of the DAMA/NaI-3 and DAMA/NaI-4 running periods are considered as quantitative examples.
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