NOVELTY - The continuous flow, reaction distillation reactor system comprises a reaction column (10), a first unit feeding vegetable oil, liquid methanol and catalyst to an upper interior of the column, a condenser (22) reclining methanol vapor for the upper interior of the column for producing condensed methanol recycled to the column upper interior and for delivering a stream of refluxed methanol liquid to the upper interior of the column, a second unit for receiving product biodiesel and liquid methanol for a lower interior of the column and for separating biodiesel in a primary product stream (33).    USE - The continuous flow, reaction distillation reactor system is useful for producing a product stream of biodiesel such as renewable fuel for diesel engines.    ADVANTAGE - The continuous flow, reaction distillation reactor system ensures effective and rapid production of biodiesel with improved selectivity, conversion and overall yield without any impurities, and allows good transesterification and recovery of biodiesel in a single system.    DETAILED DESCRIPTION - The continuous flow, reaction distillation reactor system comprises a reaction column (10), a first unit feeding vegetable oil, liquid methanol and catalyst to an upper interior of the column, a condenser (22) reclining methanol vapor for the upper interior of the column, for producing condensed methanol recycled to the column upper interior and for delivering a stream of refluxed methanol liquid to the upper interior of the column, a second unit for receiving product biodiesel and liquid methanol for a lower interior of the column and for separating biodiesel in a primary product stream (33) and returning methanol vapor to the column, and receptacle plates (11) within the column to receive the feed oil, methanol and catalyst for mixing and separating methanol vapor from oil and catalyst draining through the plates. The second unit includes a re-boiler (35) receiving the biodiesel and methanol liquid for the lower interior of the column and operating to produce methanol vapor returned to the column and biodiesel in the product stream. The column interior has a temperature of 60-65 degrees C. The feed oil and methanol are pre-heated at 57-60 degrees C. The ratio of methanol and feed oil is 3/1 (molar) for pushing transesterification to near completion. The system further includes a condenser receiving product biodiesel from the re-boiler for cooling the product stream. The re-boiler is present in direct operative communication with the lower interior of the column. An INDEPENDENT CLAIM is included for a method of producing a product stream of biodiesel.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a reaction distillation reactor system.    Reaction column (10)    Receptacle plate (11)    Condenser (22)    Second unit (31)    Product stream (33)    Re-boiler. (35)