The use and development of bias correction (BC) methods has grown fast in recent years, due to the increased demand of unbiased projections by many sectoral climate change impact applications. Case studies are frequently based on multi-variate climate indices (CIs) combining two or more essential climate variables that are frequently individually corrected prior to CI calculation. This poses the question of whether the BC method modifies the inter-variable dependencies and eventually the climate change signal. The direct bias correction of the multi-variate CI stands as a usual alternative, since it preserves the physical and temporal coherence among the primary variables as represented in the dynamical model output, at the expense of incorporating the individual biases on the CI with an effect difficult to foresee, particularly in the case of complex CIs bearing in their formulation non-linear relationships between components. Such is the case of the Fire Weather Index (FWI), a meteorological fire danger indicator frequently used in forest fire prevention and research. In the present work, we test the suitability of the direct BC approach on FWI as a representative multi-variate CI, assessing its performance in present climate conditions and its effect on the climate change signal when applied to future projections. Moreover, the results are compared with the common approach of correcting the input variables separately. To this aim, we apply the widely used empirical quantile mapping method (QM), adjusting the 99 empirical percentiles. The analysis of the percentile adjustment function (PAF) provides insight into the effect of the QM on the climate change signal. Although both approaches present similar results in the present climate, the direct correction introduces a greater modification of the original change signal. These results warn against the blind use of QM, even in the case of essential climate variables or uni-variate CIs. All the statistical downscaling experiments have been computed using the MeteoLab software (http://www.meteo.unican.es/software/meteolab), an opensource Matlab toolbox for statistical downscaling. The authors are grateful to the Spanish Meteorological Agency (AEMET) for providing the observational data and Erika Coppola from the International Center of Theoretical Physics (ICTP) and Erik van Meijgaard from the Royal Netherlands Meteorological Institute (KNMI) for making available the ENSEMBLES RegCM3 and RACMO2 regional climate models, respectively. A.C. thanks to the Spanish Ministry of Economy and Competitiveness for the funding provided within the FPI programme (BES-2011-047612). J.F. acknowledges support from the INSIGNIA project, co-funded by the Spanish R&D programme (CGL2016-79210-R) and the European Regional Development Fund. This work was partially supported by the project MULTI-SDM (CGL2015-66583-R, MINECO/FEDER). We also thank two anonymous referees for their useful comments that helped to improve the original manuscript.