Based on the magnitude–redshift diagram for the sample of supernovae Ia analyzed by Perlmutter et al. (1999), Davis & Lineweaver (2004) ruled out the special relativistic interpretation of cosmological redshifts at a confidence level of 23σ. Here, we critically reassess this result. Special relativity is known to describe the dynamics of an empty universe, by means of the Milne kinematic model. Applying only special relativistic concepts, we derive the angular diameter distance and the luminosity distance in the Milne model. In particular, in this model we do not use the underlying metric in its Robertson–Walker form, so our exposition is useful for readers without any knowledge of general relativity. We do however, explicitly use the special relativistic Doppler formula for redshift. We apply the derived luminosity distance to the magnitude–redshift diagram for supernovae Ia of Perlmutter et al. (1999) and show that special relativity fits the data much better than that claimed by Davis & Lineweaver. Specifically, using these data alone, the Milne model is ruled out only at a 2σ level. Alhough not a viable cosmological model, in the context of current research on supernovae Ia it remains a useful reference model when comparing predictions of various cosmological models.