This paper proposes a novel fault-tolerant gait for Quadruped robots using energy stability margins. The previously developed fault-tolerant gaits for quadruped robots have a drawback of having marginal stability margin, which may lead to tumbling. In the process of tumbling, the potential energy of the center of gravity goes through a maximum. The larger the difference between the potential energy of the center of gravity of the initial position and that of this maximum, the less the robot tumbles. Hence this difference of potential energy, dubbed as Energy Stability Margin (ESM), can be regarded as the stability margin. In this paper, a novel fault-tolerant gait is presented which gives positive ESM to a quadruped robot suffering from a locked joint failure. Positive ESM is obtained by adjusting foot positions between leg swing sequences. The advantage of the proposed fault-tolerant gait is demonstrated in a case study where a quadruped robot with a failed leg walks on a even slope.