The East India Coastal Current (EICC) flows equatorward during October--December carrying low salinity water from the Bay of Bengal en route. Using results from a high resolution ocean general circulation model, satellite altimeter data, Argo float profiles and ocean color images we show that the EICC bifurcates east of Sri Lanka. One part continues along the coast of Sri Lanka but the major part of the EICC, called here as the East Sri Lanka Jet (ESLJ) flows eastward into the Bay of Bengal. As a result of this bifurcation, there is offshore transport of chlorophyll a rich low salinity water from the coast of Sri Lanka. Altimeter data from 1993--2004 show that the bifurcation occurred every year except during the Indian Ocean Dipole (IOD) years of 1994 and 1997. The bifurcation occurs when an anticyclonic eddy that propagates westward ahead of a downwelling Rossby wave front impinges on the Sri Lanka coast. This new finding suggests that the main route of the low salinity water from the Bay of Bengal into the southeastern Arabian Sea may not be along the coast around Sri Lanka but through the Winter Monsoon Current.