In a vertically 2-dimensional steady adiabatic fluid system, there exists a vorticity-like conserved quantity, which is a function of the stream function. In Smith (1985)'s original model of downslope windstorm, this function is assumed to be linear, and the proportionality constant to be negative. However, the possibility of its positiveness can not be excluded. In this note, the case for the constant to be positive is examined, and the followings are shown. Also in this case, there exist solutions representing downslope windstorms. The unnatural upper bound for the atmospheric height in Smith (1985)'s solution does not emerge, and the solution may exist for any large value of the atmospheric height. The ratio of the mountain height to the atmospheric height is somewhat greater than that of Smith (1985)'s solution.