Fetal ECG (FECG) monitoring using abdominal maternal signals is a non-invasive technique that allows early detection of changes in fetal wellbeing. Several other signal components have stronger energy than the FECG, the most important being maternal ECG (MECG) and, especially during labor, uterine EMG. This study proposes a new method to subtract MECG after detecting and removing abdominal signal segments with high-amplitude variations due to uterine contractions. The method removes MECG from abdominal signals using an approximation of the current MECG segment based on a linear combination of previous MECG segments aligned on the R-peak. The coefficients of the linear model are computed so that the squared error of the approximation over the whole current segment is minimized. Abdominal signal segments strongly affected by uterine contractions are detected by applying median filtering. The methods proposed are tested on real abdominal data recorded during labor, with FECG recorded using scalp electrodes synchronously recorded for comparison.