This study presents a novel topology of a buck-boost converter that features: (i) quadratic voltage gain; (ii) positive output voltage with respect to the input; (iii) continuous input current. Moreover, as the main contribution, (iv) it features a minimum ripple design, for which input current and output voltage ripples are simultaneously cancelled at the desired operating point. It is also shown that even though the duty cycle deviates from a nominal minimum ripple point, the converter exhibits a significantly low switching ripple percentage within a full operation range. The operation mechanism, steady-state equations and overall analysis are presented. Furthermore, simulations and experiments were performed to validate the theory.