NOVELTY - Reactor for transesterification of liquids, comprises: (i) at least one module, preferably square, with an inlet and an outlet; (ii) a coupling impedance connected to activate the ultrasonic transducer; (iii) a signal generator connecting the impedance coupler; and (iv) a power supply to connect the signal generator to activate the reactor.    USE - The reactor and system are useful for transesterification of liquids; and for continuous generation of biodiesel (all claimed).    DETAILED DESCRIPTION - Reactor for transesterification of liquids, comprises: (i) at least one module, preferably square-shaped, with an inlet and an outlet; which in turn comprises a throttle valve inflow of reactants is placed at the inlet of the module; a plate is provided vertically in the center of the reactor, the inner end does not contact the rear wall of the module; a first group of fins is placed vertically and perpendicularly to the plate, where the fins are spaced apart; a second group of fins is placed vertically and perpendicularly to the side walls of the reactor, the latter being interleaved with the fins of the first group; a zigzag shaped duct, formed by the arrangement of the groups of fins, where the conduit follows a path in form of U; a throttle valve flow biodiesel and by-products are placed at the output of the module; and at least three ultrasonic transducers; where a first transducer is placed at the outer end of the plate and the other two in the rear corners of the reactor; (ii) a coupling impedance connected to activate the ultrasonic transducer; (iii) a signal generator connecting the impedance coupler; and (iv) a power supply to connect the signal generator to activate the reactor. INDEPENDENT CLAIMS are included for:    (1) a system for transesterification of liquids, comprising: (i) at least one mixer with units for preheating the raw material that is subjected to transesterification; (ii) at least one transesterification reactor which receives the mixer, and the preheated material; (iii) at least a decanter that is electric field-assisted; (iv) at least one container of glycerin; (v) at least one washing column; (vi) at least one flash type evaporator; (vii) at least one container of purified biodiesel; (viii) mainstream media provided between the modules of the system; and (ix) valves for controlling flow between the modules; and    (2) a method for continuous generation of biodiesel, which involves: (i) trans-esterification of triglycerides with a contaminated mixture of biodiesel, by differential ultrasonic cavitation of the reactants traveling through narrow channels; (ii) decanting biodiesel byproducts traveling in a section similar to the previous structure without ultrasonic cavitation; (iii) washing with resin for removal of soaps, catalyst, and free glycerol; and (iv) evaporating the residual alcohol in the flash type evaporator.