Aims: The importance of disc-disc major mergers in galaxy evolution remains uncertain. We study the major merger fraction in a SPITZER/IRAC-selected catalogue in the GOODS-S field up to z 1 for luminosity- and mass-limited samples. Methods: We select disc-disc merger remnants on the basis of morphological asymmetries/distortions, and address three main sources of systematic errors: (i) we explicitly apply morphological K-corrections; (ii) we measure asymmetries in galaxies artificially redshifted to zd = 1.0 to deal with loss of morphological information with redshift; and (iii) we take into account the observational errors in z and A, which tend to overestimate the merger fraction, though use of maximum likelihood techniques. Results: We obtain morphological merger fractions (f_m^mph) below 0.06 up to z 1. Parameterizing the merger fraction evolution with redshift as f_m^mph(z) = f_m^mph(0) (1+z)^m, we find that m = 1.8 ± 0.5 for MB ≤ -20 galaxies, while m = 5.4 ± 0.4 for Mstar ≥ 1010 M&sun; galaxies. When we translate our merger fractions to merger rates (Re_m^mph), their evolution, parameterized as Re_m^mph(z) = Re_m^mph(0) (1+z)^n, is quite similar in both cases: n = 3.3 ± 0.8 for MB ≤ -20 galaxies, and n = 3.5 ± 0.4 for Mstar ≥ 1010 M&sun; galaxies. Conclusions: Our results imply that only 8% of today's Mstar ≥ 1010 M&sun; galaxies have undergone a disc-disc major merger since z 1. In addition, 21% of Mstar ≥ 1010 M&sun; galaxies at z 1 have undergone one of these mergers since z 1.5. This suggests that disc-disc major mergers are not the dominant process in the evolution of Mstar ≥ 1010 M&sun; galaxies since z 1, with only 0.2 disc-disc major mergers per galaxy, but may be an important process at z > 1, with ˜1 merger per galaxy at 1 < z < 3.