Upon performing XPath queries on XML documents that are stored in relational databases, the execution of path expressions with steps of the star operator '*', which can be mapped to arbitrary names of either elements or attributes, has not been treated seriously in the literature. This paper presents schemes of acquiring path identifiers of query expressions that have steps of star operators in addition to steps of element names and attribute names. The contribution of this paper can be summarized as follows. First, we show that path identifiers of "/at*" and "//at*" can be obtained from the relation Path that holds path identifiers of path expressions in XML documents; by extending the relation Path, path identifiers of "//*" can be obtained from the extended relation; and some of "/*"s can be handled with the same way as "// *". Second, to obtain path identifiers of "/*" from the extended relation Path, we propose a new reserved character '$' that extends the string-pattern of the LIKE operator of SQL. The reserved character '$' followed by the restricting character string '[Apatterns]' matches arbitrary number of arbitrary characters except for the characters listed in the restricting character string.