Normalization design of XML Schemas and DTDs (document type definitions) is to produce a set of XML schemas or DTDs that can well represent data dependencies and eliminate redundancies. Now there are a few researches on it, and the existing researches are still at its initial stage. Provost proposed the idea of applying the theory of relational database to XML schemas normalization design. This idea has not been put into practice. The paper shows algorithms of hierarchical schemas design for XML schemas and DTDs normalization design based on Provost's idea. Firstly the paper analyzes hierarchy decomposition based on Provost's idea. Then it presents an algorithm producing a decomposition tree to eliminate redundant schemas. Finally it shows an algorithm of hierarchical schemas design for XML schemas and DTDs normalization design to get over deficiencies for Provost's idea. With respect to other researches on normalization design for XML schemas and DTDs, the set of full and embedded MVDs in hierarchical schemas produced by these algorithms are implied by the given set of MVDs (multivalued dependencies), and the hierarchical schemas eliminate redundant ones and satisfy the lossless join property.