The linear stability of unstably stratified shear flows between two horizontal parallel plates was investigated. Eigenvalue problems were solved numerically by making use of the expansion method in Chebyshev polynomials, and the critical Rayleigh numbers were obtained accurately in the Reynolds number range of (0.01, 100). It was found that the critical Rayleigh number increases with an increase of the Reynolds number. The result strongly supports previous stability analyses except for the analysis by Makino and Ishikawa (J. Jpn. Soc. Fluid Mech. 4 (1985) 148 - 158) in which a decrease of the critical Rayleigh number was obtained.