We present a concept of an electromagnetic phase-shift flowmeter that has a significantly reduced sensitivity to the variation of the electrical conductivity of a liquid metal. A simple theoretical model of the flowmeter is considered where the flow is approximated by a solid finite-thickness conducting layer which moves in the presence of an ac magnetic field. In contrast to the original design [Priede et al., Meas. Sci. Technol. 22 (2011) 055402], where the flow rate is determined by measuring only the phase shift between the voltages induced in two receiving coils, the improved design measures also the phase shift between the sending and the upstream receiving coils. These two phase shifts are referred to as internal and external ones, respectively. We show that the effect of electrical conductivity on the internal phase shift, which is induced by the flow, can be strongly reduced by rescaling it with the external phase shift, which depends mostly on the conductivity of medium. Two different rescalings are found depending on the ac frequency. At low frequencies, when the shielding effect is weak, the effect of conductivity is strongly reduced by rescaling the internal phase shift with the external one squared. At higher frequencies, the same is achieved by rescaling the internal phase shift directly with the external one.