Unsupervised pre-training has been on the lookout for the virtue of a value function representation referred to as successor features (SFs), which decouples the dynamics of the environment from the rewards. It has a significant impact on the process of task-specific fine-tuning due to the decomposition. However, existing approaches struggle with local optima due to the unified intrinsic reward of exploration and exploitation without considering the linear regression problem and the discriminator supporting a small skill sapce. We propose a novel unsupervised pre-training model with SFs based on a non-monolithic exploration methodology. Our approach pursues the decomposition of exploitation and exploration of an agent built on SFs, which requires separate agents for the respective purpose. The idea will leverage not only the inherent characteristics of SFs such as a quick adaptation to new tasks but also the exploratory and task-agnostic capabilities. Our suggested model is termed Non-Monolithic unsupervised Pre-training with Successor features (NMPS), which improves the performance of the original monolithic exploration method of pre-training with SFs. NMPS outperforms Active Pre-training with Successor Features (APS) in a comparative experiment.