Novelty and appropriateness are considered the two fundamental features of creative thinking, including insight problem solving, which can be performed through chunk decomposition and constraint relaxation. Based on a previous study that separated the neural bases of novelty and appropriateness in chunk decomposition, in this study, we used event-related functional magnetic resonance imaging (fMRI) to further dissociate these mechanisms in constraint relaxation. Participants were guided to mentally represent the method of problem solving according to the externally provided solutions that were elaborately prepared in advance and systematically varied in their novelty and appropriateness for the given problem situation. The results showed that novelty processing was completed by the temporoparietal junction (TPJ) and regions in the executive system (dorsolateral prefrontal cortex [DLPFC]), whereas appropriateness processing was completed by the TPJ and regions in the episodic memory (hippocampus), emotion (amygdala), and reward systems (orbitofrontal cortex [OFC]). These results likely indicate that appropriateness processing can result in a more memorable and richer experience than novelty processing in constraint relaxation. The shared and distinct neural mechanisms of the features of novelty and appropriateness in constraint relaxation are discussed, enriching the representation of the change theory of insight.