The joint dispatch of regional electricity markets can improve the overall economic efficiency of interconnected markets by increasing the combined social welfare of the interconnected markets. This paper presents a new decentralized optimization technique based on Augmented Lagrangian Relaxation (ALR) to perform the joint dispatch of interconnected electricity markets. The Block Coordinate Descent (BCD) technique is applied to decompose the inseparable quadratic term of the augmented Lagrangian equation into individual market optimization problems. The Interior Point/Cutting Plane (IP/CP) method is used to update the Lagrangian multiplier in the decomposed market optimization problem. The numerical example is presented to validate the effectiveness of the proposed decentralized method.