We present a statistical study on reconnection occurrence at the dayside magnetopause performed using the Double Star TC1 plasma and magnetic field data. We examined the magnetopause crossings that occurred during the first year of the mission in the 0600–1800 LT interval and we identified plasma flows, at the magnetopause or in the boundary layer, with a different velocity with respect to the adjacent magnetosheath. We used the Walén relation to test which of these flows could be generated by magnetic reconnection. For some event we observed opposite‐directed reconnection jets, which could be associated with the passage of the X‐line near the satellite. We analyzed the occurrence of the reconnection jets and reconnection jet reversals in relation to the magnetosheath parameters, in particular the local Alfvèn Mach number, the plasma β, and the magnetic shear angle. We also studied the positions and velocities of the reconnection jets and jet reversals in relation to the magnetosheath magnetic field clock angle. We found that the observations indicate the presence of a reconnection line hinged near the subsolar point and tilted according to the observed magnetosheath clock angle, consistently with the component merging model.