We consider a modified Randall-Sundrum metric model in a five-dimensional spacetime. The metric is conformally flat, has an exponential warp factor, and is physically distinct from the original Randall-Sundrum metric model. Massless scalar fields are localized on the brane for decreasing warp factor while massive scalar fields are localized on the brane for either decreasing or increasing warp factors. There is an upper bound mass for the decreasing warp factor and there are two possible different masses for the increasing warp factor. For a constant value of the fifth component of the vector matter field we obtain a possible localization for massless vector fields, but not for massive vector fields. Both massless and massive spinor fields unfortunately are not localized on the brane.