Recently, many methods have appeared to solve the problem of the evolution of alignment under the change of ontologies. The main challenge for them is to maintain consistency of alignment after applying the change. An alignment is consistent if and only if the ontologies remain consistent even when used in conjunction with the alignment. The objective of this work is to take a step forward by considering the alignment evolution according to the conservativity principle under the change of ontologies. In this context, an alignment is conservative if the ontological change should not introduce new semantic relationships between concepts from one of the input ontologies. The authors give methods for the conservativity violation detection and repair under the change of ontologies and they carry out an experiment on a dataset adapted from the Ontology Alignment Evaluation Initiative. The experiment demonstrates both the practical applicability of the proposed approach and shows the limits of the alignment evolution methods compared to the alignment conservativity under the change of ontologies.