The paper considers non-destructive testing (NTDs) as a means to solve the flaw detection problems of magnetic products. It proposes a new probe-coil magnetic-field NDT, not requiring the pre-magnetization of the test object material, which is mandatory for all conventional magnetic flaw detection techniques. A new bifactor excitation of the fluxgate sensor’s sensitive element, based on double μ-transformation through the simultaneous activation of magnetic-modulating and electromagnetic-acoustic effects, is theoretically justified. The physical processes underlying the proposed technique are considered in detail, and a scheme for its practical implementation is described. The authors provide a variant of the new fluxgate’s original design, implementing the proposed excitation technique. The specifics of implementing the fluxgate operating modes are analyzed, testifying to the possibility of detecting a given class of flaws with the required coverage as well as ensuring the required diagnostic resolution during flaw detection, which, in fact, indicates a more reliable identification of both the flaw type and location. Herewith, the new fluxgate type features the advantages of improved functionality and lower cost due to its simple design. The paper also considers a method to experimentally study the capabilities of the proposed fluxgate sensor with a new bifactor excitation in detail. The results of the experimental study into its key specifications are provided, confirming its high resolution, narrower zone of uncertainty, and the possibility of detecting smaller flaws at greater depths compared to available analogs.