This study proposes a fault-tolerant scheme for an impedance-sourced cascaded H-bridge (CHB) converter that can fully restore the converter operation to the pre-fault conditions without any hardware intervention. The proposed faulttolerant scheme has three key elements: a new quasi-z-source CHB converter, a modified modulation method for the introduced z-source CHB, and a modified implementation of the fundamental phase shift compensation (FPSC) method. In case of a fault on one of the inverter switches, the proposed fault-tolerant scheme enables the z-source CHB to generate balanced line-to-line voltages with the same amplitude as the pre-fault voltages, while evenly distributing an inevitable voltage stress increase over all converter switches. In this study, first a brief review of CHB converters and the FPSC method is provided. Then the proposed fault-tolerant scheme is introduced. Finally, several experimental results from a prototype converter are provided to validate the operation of the proposed strategy.