We examined bisection of lines viewed in only one hemifield by normal subjects. Subjects first performed a traditional version of line bisection, by indicating the perceived midpoint of a line on paper with a penmark. Bisection was accurate when they were allowed to shift their gaze over the stimulus, but it was biased towards the central visual field (centripetally) when gaze was fixed so that the line was seen in only one hemifield. In a second experiment, lines with transectors at various locations were presented briefly on a screen and subjects had to indicate on which side of the perceived midpoint the transector was located. A centripetal bias was still found, indicating that it has a perceptual origin. The interaction between bias and effects of tangent line presentation suggested that subjects were performing an angle bisection rather than a line bisection. Also, there was bias in not only right and left hemifields but also upper and lower hemifields. In a third experiment, increasing the width of the stimulus bars peripherally did not eliminate this bias. Bias was size-invariant along the horizontal meridian. This spatial version of Weber's law was modeled by a magnification function using an exponential equation. The slope of this function is much shallower than those currently known for V1, V4 and V5. We conclude that a centripetal bias exists for hemifield line bisection and that this bias likely contributes to the contralateral bias of line bisection by hemianopic patients found in other studies.