In recent years, multiple technologies have been proposed with the aim of combining the characteristics of traditional planar and non-planar transmission lines. The first and most popular of these technologies is the Substrate Integrated Waveguide (SIW), where rows of metallic vias are mechanized in a printed circuit board (PCB). These vias, together with the top and bottom metal layers of the PCB, form a channel for the propagation of the electromagnetic fields, similar to that of a rectangular waveguide, but through a dielectric body, which increases the losses. To reduce these losses, the empty substrate integrated waveguide (ESIW) was recently proposed. In the ESIW, the dielectric is removed from the substrate, and this results in better performance (low profile and easy manufacturing as in SIW, but lower losses and better quality factor for resonators). Recently, to increase the operational bandwidth (monomode propagation) of the ESIW, the ridge ESIW (RESIW) and a transition from RESIW to microstrip line was proposed. In this work, a new and improved wideband transition from microstrip line (MS) to RESIW, with a dielectric taper based on the equations of the superellipse, is proposed. The new wideband transition presents simulated return losses in a back-to-back transition greater than 20 dB in an 87% fractional bandwidth, while in the previous transition the fractional bandwidth was 82%. This is an increment of 5%. In addition, the transition presents simulated return losses greater than 26 dB in an 84% fractional bandwidth. For validation purposes, a back-to-back configuration of the new transition was successfully manufactured and measured. The measured return loss is better than 14 dB with an insertion loss lower than 1 dB over the whole band.