By the combination of high-speed imaging and numerical simulation, we explore the hydrodynamics and possible morphologies of the entire coalescence of a pendent droplet and sessile one. We identify three types of coalescence morphologies and plot a corresponding phase diagram to identify them depending on the Bond number and the size ratio between the two droplets. In addition to the well-known linear inertial growth of the liquid bridge at the initial contact of the two drops, we observe a new subsequent slower linear expansion of the liquid bridge and provide a linear scaling law with a measured prefactor to quantitatively represent it. This new growth is found to be due to the transition of the capillary force produced by a change in the azimuthal surface profile of the liquid bridge.