High-precision measurement of half-life and Q(alpha) value of neutral and highly charged alpha emitters is a major subject of investigation currently. In this framework, we recently pushed half-life measurements of neutral emitters to a precision of a few per mil. This result was achieved by using different techniques and apparatuses at Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud (INFN-LNS) and GSI Darmstadt. Here we report on Fr-213 half-life determination [T-1/2(Fr-213) = 34.14 +/- 0.06 s] at INFN-LNS, detailing the measurement protocol used. Direct comparison with the accepted value in the literature shows a discrepancy of more than three sigma. We propose this new value as a reference, discussing previous experiments.