The opening of the Equatorial and South Atlantic Oceans is still a matter of debate, particularly as concerns the locations of the intraplate deformation. We propose here a critical review of the kinematic models published since Bullard et al., 1965, based on a series of constraints: new interpretation of the magnetic anomalies, seafloor isochrons, flow lines, fracture zones, continental and oceanic homologous structures and radiometric dating of igneous rocks. All of these models present numerous unexplained misfits (gaps, overlaps and misalignments). We present here a new evolution of the Equatorial and South Atlantic Ocean from the tightest reconstruction to Chron C34. This new model confirms the hypothesis of a northward propagation of the South American deformation proposed by Eagles, but rejuvenates slightly the ages for this propagation and refines the plate reconstructions. In particular, we highlight the role of the kinematic "buffer" Santos block, located between the salty Aptian Central segment in the North and the Volcanic Hauterivian Austral segment in the South. The new initial fit presented in this study represents the tightest reconstruction that could be obtained and constitutes the base canvas on which the problem of the continental margin genesis should be addressed.