Right hemisphere injuries often produce contralesional hemispatial neglect (CN). In contrast to CN, some patients with right hemisphere damage can also show so-called ipsilesional neglect (IN). Previous reports found that patients tend to show IN on line bisection tasks but CN on other tasks such as target cancellation. To learn why these two tasks induce different spatial biases in patients with right hemisphere injury, conventional (i.e. solid) line bisection was compared with two novel bisection tasks consisting of horizontally aligned strings of characters. The subjects' task was to mark a target character that was at or closest to the true midpoint of the simulated line. Four of the 5 patients showed a dissociation whereby IN occurred for solid lines while CN was observed on character lines. The two patients assessed with an antisaccade paradigm showed a 'visual grasp' for leftward stimuli. The present results suggest that neglect on line bisection may reflect two opposing forces, an approach behavior or 'visual grasp' toward left hemispace and an attentional bias toward right hemispace.