After having announced the statistically significant observation (5.6s) of the new exotic pi K atom, the DIRAC experiment at the CERN proton synchrotron presents the measurement of the corresponding atom lifetime, based on the full pi K data sample: tau = (5.5(-2.8)(+5.0)) x 10(-15) s. By means of a precise relation (approximate to 1%) between atom lifetime and scattering length, the following value for the S-wave isospin-odd pi K scattering length a(0)(-) = 1/3 (a(1/2) - a(3/2)) has been derived: |a(0)(-)| = (0.072(-0.020)(+0.031)) M-pi(-1).