When a liquid is supplied through a nozzle onto a relatively non-wetting inclined solid surface, a narrow rivulet forms. There exist several regimes of rivulet flow depending on various flow conditions. In this paper, the fundamental mechanism behind the transition of a linear rivulet to a droplet flow is investigated. The experiments show that the droplet flow emerges due to the necking of a liquid thread near the nozzle. Based on the observation, it is argued that when the retraction velocity of a liquid thread exceeds its axial velocity, the bifurcation of the liquid thread occurs, and this argument is experimentally verified.