  Traditionally, ground-based spectrophotometric observations probing
transiting exoplanet atmospheres have employed a linear map between comparison
and target star light curves (e.g. via differential spectrophotometry) to
correct for systematics contaminating the transit signal. As an alternative to
this conventional method, we introduce a new Gaussian Processes (GP)
regression-based method to analyse ground-based spectrophotometric data. Our
new method allows for a generalised non-linear mapping between the target
transit light curves and the time series used to detrend them. This represents
an improvement compared to previous studies because the target and comparison
star fluxes are affected by different telluric and instrumental systematics,
which are complex and non-linear. We apply our method to six Gemini/GMOS
transits of the warm (T$_{\rm eq}$ = 990 K) Neptune HAT-P-26b. We obtain on
average $\sim$20 % better transit depth precision and residual scatter on the
white light curve compared to the conventional method when using the comparison
star light curve as a GP regressor and $\sim$20% worse when explicitly not
using the comparison star. Ultimately, with only a cost of 30% precision on the
transmission spectra, our method overcomes the necessity of using comparison
stars in the instrument field of view, which has been one of the limiting
factors for ground-based observations of the atmospheres of exoplanets
transiting bright stars. We obtain a flat transmission spectrum for HAT-P-26b
in the range of 490-900 nm that can be explained by the presence of a grey
opacity cloud deck, and indications of transit timing variations, both of which
are consistent with previous measurements.
