A recursive additive complement network (RacNet) is introduced to segment cell membranes in histological images as closed lines. Segmenting cell membranes as closed lines is necessary to calculate cell areas and to estimate N/C ratio, which is useful to diagnose early hepatocellular carcinoma. The RacNet is composed of a complement network and an element-wise maximization (EWM) process and is recursively applied to the network output. The complement network complements the lacking parts of cell membranes. The network, however, has a tendency to mistakenly delete some parts of the segmented cell membranes. The EWM process eliminates this unwanted effect.Experiments carried out using unstained hepatic sections showed that the accuracy for segmenting cell membranes as closed lines was significantly improved by using the RacNet.Three imaging methods, bright-field, dark-field, and phase-contrast, were used, as unstained sections show very low contrast in the bright-field imaging commonly used in pathological diagnosis. These imaging methods are available in optical microscopes used by pathologists. Among the three methods, phase-contrast imaging showed the highest accuracy.