The effect of compressibility of fluids on the instability of a liquid sheet issued from a nozzle into an ambient gas is investigated by use of linear stability analysis. It is found that increasing the gas Mach number from subsonic to transonic causes the maximum growth rate, dominant wave number, and cut-off wave number of disturbances to increase. Liquid compressibility has a minimal effect on instability. At a constant wave number, the growth rate of disturbances increases as the gas Mach number tends to 1 and then begins to decline with further increase in the gas Mach number. Hence, liquid sheet breakup is due to surface disintegration not gross fracturing in agreement with experimental observations. At small values of wave number, antisymmetrical disturbances grow faster than symmetrical ones while the growth rate of both types of disturbances approach each other at large wave numbers. At small Weber number, antisymmetrical disturbances exhibit a higher maximum growth rate and a lower dominant wave number than symmetrical disturbances. However, the maximum growth rate and dominant wave number of the two types of disturbances are almost identical when Weber number becomes large. An increase in the gas-to-liquid density ratio enhances the instability. Surface tension always opposes the development of instability.