Recent success of Knowledge Graph has spurred widespread interests in methods for the problem of Knowledge Graph completion. However, efforts to understand the quality of the candidate triples from these methods, in particular from the schema aspect, have been limited. Indeed, most existing Knowledge Graph completion methods do not guarantee that the expanded Knowledge Graphs are consistent with the ontological schema of the initial Knowledge Graph. In this work, we challenge the silver standard method, by proposing the notion of schema-correctness. A fundamental challenge is how to make use of different types of Knowledge Graph completion methods together to improve the production of schema-correct triples. To address this, we analyse the characteristics of different methods and propose a schema aware iterative approach to Knowledge Graph completion. Our main findings are: (i) Some popular Knowledge Graph completion methods have surprisingly low schema-correctness ratio; (ii) Different types of Knowledge Graph completion methods can work with each other to help overcame individual limitations; (iii) Some iterative sequential combinations of Knowledge Graph completion methods have significantly better schema-correctness and coverage ratios than other combinations; (iv) All the MapReduce based iterative methods outperform involved single-pass methods significantly over the tested Knowledge Graphs in terms of productivity of schema-correct triples. Our findings and infrastructure can help further work on evaluating Knowledge Graph completion methods, more fine-grained approaches for schema aware iterative knowledge graph completion, as well as new approximate reasoning approaches based Knowledge Graph completion methods.