The classical attribute reduction algorithm and its extended algorithms base on information system with decision attributes and can not be applied to attribute reduction for information system without decision attributes. So, based on rough set theory, this paper studied attribute reduction for information system without decision attributes in domain division of set theory and presented a heuristic attribute reduction algorithm. To a certain extent, the algorithm can resolve the attribute reduction problem for information system without decision attributes and extend application of Rough Set Theory. The analysis of the realistic example shows that the algorithm is effective and feasible.