Subcontractors depend heavily on their prime contractor and thus find it very risky to enter a new business on their own. This study proposes a framework for these subcontractors to develop blue ocean technologies related to their prime contractor. First, the primary technologies predicted to be promising are extracted from the business reports of the prime contractor. Sub-technologies are then selected through a patent-based search using keywords and International Patent Classification codes of the primary technologies. From them, blue ocean technologies are proposed by optimizing the weighted mean of the min-max normalized market value, degree of competition in the technology market, and subcontractors' potential technological capabilities for each sub-technology. This study shows that subcontractors can enhance their technology competitiveness by finding a low-risk blue ocean technology. Our empirical research on the subcontractors of a semiconductor firm identified technological patent fields for them to pursue. From our framework, subcontractors can identify blue ocean technologies by considering their prime contractor's future industrial areas and technologies of interest as well as their own technological capabilities. Furthermore, the prime contractors can gain the synergy effect of technology expansion through cooperation.