In this paper we present a two-sector real business cycle (RBC) model with one sector whose production function is with increasing return-to-scale occurring as a consequence of production externalities. We also redefine the leisure as production output from both labor and capital input as well. The findings show that indeterminacy would not exist in such specific models' setting. Moreover, this result may suggest that the common notion where a two-sector model would be easier to generate indeterminacy than a one-sector model would not stand for some special settings.