The principle of multiple input/output inversion theorem (MINT) has been employed for multi-channel equalization. In this work, we propose to partition a single-input multiple-output system into two subsystems. The equivalence between the deconvoluted signals of the two subsystems is termed as auto-relation and we subsequently exploit this relation as an additional constraint to the existing adaptive MINT algorithm. In addition, we provide analysis of the auto-relation constraint and show that this constraint confines the solution of equalization filters within a multi-dimensional space. We also explain through the use of convergence analysis why our proposed algorithm can achieve a higher rate of convergence compared to the existing MINT-based algorithms. Simulation results, using both synthetic and recorded channel impulse responses, show that our proposed auto-relation aided MINT algorithm can achieve a fast convergence compared to the existing MINT-based algorithms.