Colour correction is the mapping of device-dependent RGBs to device-independent standard CIE XYZs. Due to the nature of colour image formation and the existence of metamerism, this mapping is inherently one-to-many and thus ill-posed. However, normally it is solved for through an error-minimising linear one-to-one transform.In this paper we propose to make use of a definition of metamerism while maintaining the simplicity of a linear transform in defining an error-less colour correction. We say that a mapping is error-less if the RGB-XYZ pair put in correspondence through this mapping is such that a real, physically realisable reflectance that induces this pair exists. We show how we can solve for such a mapping using constrained linear least squares optimisation. However, since this problem is highly constrained, we introduce a notion of error in our calculations, building on a paramer set instead (the set of reflectances that map to a small uniform region in RGB space). We show that as little as 0.5% error is sufficient for a solution to exist.We find that the metamer set constrained linear colour correction works equally well as ordinary linear least squares in terms of the mean and median CIE ΔE, however reduces the overall maximum significantly. We also show that unconstrained linear least squares is not error-less. In particular, those samples that are not error-less are saturated samples, for which the metamer set constrained method reduces the mean, median as well as maximum error dramatically.