Surface nuclear magnetic resonance (NMR) is a relatively novel and powerful geophysical technique for investigating hydrological characteristics of shallow aquifers from the Earth's surface in a non-invasive way. Large current loops of approximately 100 m diameter laid on the ground transmit electromagnetic pulses into the subsurface. These pulses excite spins of protons in groundwater molecules out of their equilibrium state in the Earth's magnetic field. The spin response is recorded on either coincident or offset surface receiver loops of similar dimension. The amplitudes of the response signals recorded after single-pulse excitation provide estimates of water-content in the shallow subsurface. Another important parameter is the NMR relaxation time T(1), from which information on pore structure or even hydraulic conductivity can be inferred under favorable circumstances. T(1) data are conventionally acquired using a scheme that involves two sequential pulses of electromagnetic energy, the second of which is phase-shifted by pi relative to the first. We show that common imperfections in the transmitted pulses and variations of the excitation field with distance from the transmitter introduce significant bias in conventional estimates of T(1). Here, we propose a novel yet simple modification to the conventional scheme that is theoretically capable of resolving this problem. The proposed scheme comprises a conventional double-pulse sequence followed by an additional double-pulse sequence for which the 2nd pulse is in-phase with the 1st pulse. Subtracting the voltage signals measured during the two double-pulse sequences (i.e., phase cycle) eliminates the bias. This strategy of continuously cycling the phase of the 2nd pulse between pi and 0 in sequential double-pulse experiments and then subtracting the resulting voltages is a promising step towards recording more reliable T(1) data under general field conditions.