The actual magnetic induction waveform of cores in electrical machines is not sinusoidal i.e. higher harmonics are always included. Thus the core loss in actual electrical machines is different from the core loss which is measured by the standard method, because the waveform of magnetic induction should be sinusoidal in the standard testing method. Core loss analysis under higher harmonic induction is always important in electric machine design. In this works we measured the core loss when a hysteresis loop has only one period of an ac minor loop of higher harmonic frequency, depending on the position of the ac minor loop of relative to the fundamental harmonic frequency. From this experiment, the core loss P(B₀f₀, B_h, nf₀) under a higher harmonic magnetic induction B_h could be expressed by the linear combination the core loss at fundamental harmonic frequency P_c(B₀, f₀), the core loss of ac minor loop at zero induction region of the major hysteresis loop P_cL(B_h, nf₀), and the core loss of an ac minor loop in the high induction region of the major hysteresis loop P_cH(B_h, nf₀) i.e., P_c(B₀, f₀, B_h, nf₀)=P_c(B₀, f₀)+(n-1)[k₁(B₀)) P_cL(B_h, nf₀)+(1-k₁(B₀)) P_cH (B_h, nf₀)]. This will be useful formula for electrical machine designers and one of effective methods to predict core loss including higher harmonic induction.