During solar flares Hα ribbons form and often move away from the local magnetic polarity inversion line (PIL). While the motion perpendicular to the PIL has been taken as evidence for coronal magnetic reconnection in the so-called CSHKP standard model, the other velocity component parallel to the PIL is much less adopted as a property of the magnetic reconnection process. In this Letter we report an event in which the motion parallel to the PIL is found in both Hα ribbons and a thermal hard X-ray source. Such commonality would indicate a link between the coronal magnetic reconnection and footpoint emissions as in the standard solar flare model. However, its direction implies a reconnection region that is increasing in length, a feature missing from the standard two-dimensional model. We present a modified framework in which the variation along the third dimension is allowed, in order to assess the effect of such a proper motion on estimation of the magnetic reconnection rate. Data used are hard X-ray maps from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), Hα filtergrams of Big Bear Solar Observatory (BBSO), and the SOHO Michelson Doppler Imager (MDI) magnetogram obtained for the 2004 March 30 flare.