System for the non-destructive testing of components, in which two ultrasonic transducers (1, 2), which form a pair and each have a piezoelectric ceramic plate-shaped element (1.1, 2.1) with a rectangular geometry, which are formed on two opposite surfaces each with an electrode (1.2, 2.2), can be fastened to a surface of a component, wherein the two ultrasonic transducers (1, 2) in the pair are arranged at a distance from one another such that there is no direct mechanical contact and the two ultrasonic transducers (1, 2) in the pair are arranged beside one another with a parallel orientation of their central longitudinal axes, wherein each of the central longitudinal axes are also parallel to the edges of the piezoelectric ceramic plate-shaped elements (1.1, 2.1) having a width b, and the two piezoelectric ceramic plate-shaped elements (1.1, 2.1) have a different polarization along their width b, wherein the width b corresponds to a longer edge length of the rectangular geometry of the piezoelectric ceramic plate-shaped elements (1.1, 2.1) and the two ultrasonic transducers (1, 2) in the pair are connected in this case with the same polarity to an electrical voltage source which can be operated in a pulsed manner, or the two piezoelectric ceramic plate-shaped elements (1.1, 2.1) have an identical polarization along their width b, and the two ultrasonic transducers (1, 2) in the pair are connected in this case with opposite polarity to an electrical voltage source which can be operated in a pulsed manner, and the electrical voltage source is designed to apply electrical voltages in the frequency range of 10 kHz to 1 MHz to the two ultrasonic transducers (1, 2), and at least one of the two ultrasonic transducers (1, 2) in the pair and/or at least one further ultrasonic transducer arranged at a known distance from the two ultrasonic transducers (1, 2) in the pair is/are designed to detect ultrasonic waves reflected by defects on the component and/or shear waves simultaneously emitted by the two ultrasonic transducers (1, 2) in the pair, and the detected ultrasonic waves can be transmitted to an electronic evaluation and control unit, wherein the electronic evaluation unit is designed to evaluate the detected ultrasonic waves with respect to their amplitude and/or their temporal sequence. the two ultrasonic transducers (1, 2) in the pair are arranged at a distance from one another such that there is no direct mechanical contact and the two ultrasonic transducers (1, 2) in the pair are arranged beside one another with a parallel orientation of their central longitudinal axes, wherein each of the central longitudinal axes are also parallel to the edges of the piezoelectric ceramic plate-shaped elements (1.1, 2.1) having a width b, and the two piezoelectric ceramic plate-shaped elements (1.1, 2.1) have a different polarization along their width b, wherein the width b corresponds to a longer edge length of the rectangular geometry of the piezoelectric ceramic plate-shaped elements (1.1, 2.1) and the two ultrasonic transducers (1, 2) in the pair are connected in this case with the same polarity to an electrical voltage source which can be operated in a pulsed manner, or the two piezoelectric ceramic plate-shaped elements (1.1, 2.1) have an identical polarization along their width b, and the two ultrasonic transducers (1, 2) in the pair are connected in this case with opposite polarity to an electrical voltage source which can be operated in a pulsed manner, and the electrical voltage source is designed to apply electrical voltages in the frequency range of 10 kHz to 1 MHz to the two ultrasonic transducers (1, 2), and at least one of the two ultrasonic transducers (1, 2) in the pair and/or at least one further ultrasonic transducer arranged at a known distance from the two ultrasonic transducers (1, 2) in the pair is/are designed to detect ultrasonic waves reflected by defects on the component and/or shear waves simultaneously emitted by the two ultrasonic transducers (1, 2) in the pair, and the detected ultrasonic waves can be transmitted to an electronic evaluation and control unit, wherein the electronic evaluation unit is designed to evaluate the detected ultrasonic waves with respect to their amplitude and/or their temporal sequence.