Enabling future electrification of air and ground transportation requires flexible, compact, and highly efficient power converters. Four-switch non-inverting buck-boost dc-dc converters allow for wide and overlapping input and output voltage ranges, enabling integration of fuel cells and batteries whose voltages vary with state of charge and operating conditions. In this work, we propose a novel non-mirrored buck-boost (N-MBB) Flying Capacitor Multilevel (FCML) dcdc converter. The proposed topology integrates the conventionally separated buck and boost bridge-legs, which is enabled by novel monolithic bidirectional GaN transistors. Compared to the conventional mirrored buck-boost FMCL converter, the proposed topology shows a higher inductor volume but advantageously a lower component count, better utilization of the installed chip area and flying capacitors, and lower conduction losses. The final paper will contain a detailed description of the operation modes, a comparative evaluation regarding component stresses, and discuss topology variations with adjusted trade-offs and even dc-ac conversion functionality.