We report results from a new measurement of the K-e4 decay K-+/- -> pi(+)pi(-)e(+/-)nu by the NA48/2 collaboration at the CERN SPS, based on a partial sample of more than 670 000 K-e4 decays in both charged modes collected in 2003. The form factors of the hadronic current (F,G,H) and pi pi phase difference (delta=delta(s)-delta(p)) have been measured in ten independent bins of the pi pi mass spectrum to investigate their variation. A sizeable acceptance at large pi pi mass, a low background and a very good resolution contribute to an improved experimental accuracy, a factor two better than in the previous measurement, when extracting the pi pi scattering lengths a(0) (0) and a(0) (2). Under the assumption of isospin symmetry and using numerical solutions of the Roy equations, the following values are obtained in the plane (a(0) (0),a(0) (2)): a(0) (0)=0.233 +/- 0.016(stat)+/- 0.007(syst),a(0) (2)=-0.0471 +/- 0.011(stat)+/- 0.004syst. The presence of potentially large isospin effects is also considered and will allow comparison with precise predictions from Chiral Perturbation Theory.