Metamorphic testing is a testing method for problems without test oracles. Integration testing allows for detecting errors in complex systems that may not be found during the testing of their components. In this paper, we propose a novel approach that applies metamorphic testing in integration testing. The main idea is to develop a composite metamorphic relation for the system represented as an acyclic graph. This relation is a logical function of metamorphic relations for the parts of the system (vertices of the graph). It takes into account the features of the parts. Also, it can simplify the search for failure by identifying the subsystem with error. In this paper's theoretical part, we describe an algorithm of relation design. Then, we apply our method to a bioinformatics system for comparative genetic analysis of tissues using production tools. This experiment proves our method can be applied to real-life pipelines and find errors in them.