The selected bit line in a non-volatile memory carries a cell conduction current to be measured and also a leakage current or noise due to weak coupling with neighboring array structures. In a first phase, a sense amplifier senses the bit line current by discharging a capacitor with the combined current (cell conduction current plus the leakage current) over a predetermined time. In a second phase, the cell conduction current is minimized and significantly the leakage current in the selected bit line is used to recharge in tandem the capacitor in a time same as the predetermined time, effectively subtracting the component of the leakage current measured in the first sensing phase. The resultant voltage drop on the capacitor over the two sensing phases provides a measure of the cell conduction current alone, thereby avoiding reading errors due to the leakage current present in the selected bit line.