Recently, model merging techniques have surfaced as a solution to combine multiple single-talent models into a single multi-talent model. However, previous endeavors in this field have either necessitated additional training or fine-tuning processes, or require that the models possess the same pre-trained initialization. In this work, we identify a common drawback in prior works w.r.t. the inconsistency of unit similarity in the weight space and the activation space. To address this inconsistency, we propose an innovative model merging framework, coined as merging under dual-space constraints (MuDSC). Specifically, instead of solely maximizing the objective of a single space, we advocate for the exploration of permutation matrices situated in a region with a unified high similarity in the dual space, achieved through the linear combination of activation and weight similarity matrices. In order to enhance usability, we have also incorporated adaptations for group structure, including Multi-Head Attention and Group Normalization. Comprehensive experimental comparisons demonstrate that MuDSC can significantly boost the performance of merged models with various task combinations and architectures. Furthermore, the visualization of the merged model within the multi-task loss landscape reveals that MuDSC enables the merged model to reside in the overlapping segment, featuring a unified lower loss for each task. Code and models will be made publicly available.