Intermediate fine mapping has received considerable attention recently, with the goal of providing statistically precise and valid chromosomal regions for fine mapping following initial identification of broad regions that are linked to a disease. The following classes of methods have been proposed and compared in the literature: (1) LOD-support intervals, (2) generalized estimating equations, (3) bootstrap, and (4) confidence set inference framework. These methods provide confidence intervals either with coverage levels deviating from the nominal confidence levels or that are not fully efficient. Here, we propose a novel Bayesian method for constructing such intervals using affected sibling pair data. The susceptibility gene location is treated as a parameter in this method, with a uniform prior. A Metropolis-Hastings algorithm is implemented to sample from the posterior distribution and highest posterior density intervals of the disease gene locations are constructed. Correct coverage levels are maintained by our method. Both simulation studies and an application to a rheumatoid arthritis dataset demonstrate the improved efficiency of the Bayesian intervals compared with existing methods.