The large systematic deviations in haptic parallelity matching are most likely due to the biasing influence of the hand-centered egocentric reference frame. Previous results showed that eliminating or reducing this bias resulted in smaller deviations, with significantly larger effects observed in female participants. The current study investigated the effect of reducing the egocentric bias in a pure haptic condition. Blind-folded male and female participants had to feel the orientation of a reference bar with their non-dominant hand and to parallel this orientation on a test bar with their dominant hand. In one condition, they were instructed to use their flat-stretched hand to feel and match the bars, while in the other condition (HPF), they were instructed to set the test bar while gripping the bar with the fingers and thumb. It was hypothesized that the latter would reduce the biasing influence of the hand-centered egocentric reference frame. Results showed that this was indeed the case. Deviations were significantly smaller for HPF; however, this effect was the same in both genders. The previously observed gender effect, showing a significantly larger improvement for women when reducing the influence of the egocentric reference frame, was not replicated.