The present work reports experimental results concerning the specific isobaric heat capacity of pure water at elevated pressure. Experiments were performed using a Tian-Calvet differential scanning calorimeter (Setaram Model BT2.15), at temperatures ranging from 298.15 to 465.65 K and at a constant pressure of 4.0 MPa. The aim of this study is to compare the new experimental results with values predicted by the IAPWS-95 formulation, which is generally accepted as reliable by the scientific community despite the fact that, in this formulation, nearly all the data for the isobaric heat capacity of water are based on measurements of Sirota's group in the former Soviet Union in the period from 1956 to 1970. The present calorimetric results for the specific heat capacity of pure water were found to be substantially in disagreement with the values obtained using the IAPWS-95 formulation, especially at high temperatures, where the differences are greater than 20%. Additional studies are therefore warranted in order to confirm this discrepancy.