Because direct measurements of the refractive index of hemoglobin over a large wavelength range are challenging, indirect methods deserve particular attention. Among them, the Kramers-Kronig relations are a powerful tool often used to derive the real part of a refractive index from its imaginary part. However, previous attempts to apply the relations to solutions of human hemoglobin have been somewhat controversial, resulting in disagreement between several studies. We show that this controversy can be resolved when careful attention is paid not only to the absorption of hemoglobin but also to the dispersion of the refractive index of the nonabsorbing solvent. We present a Kramers-Kroning analysis taking both contributions into account and compare the results with the data from several studies. Good agreement with experiments is found across the visible and parts of near-infrared and ultraviolet regions. These results reinstate the use of the Kramers-Kronig relations for hemoglobin solutions and provide an additional source of information about their refractive index.