Thin film of isothermal Newtonian fluids lying on the(x,y)plane can be extended without generating thickness nonuniformity when the film is initially uniform in thickness and the velocity fieldvx(x,y,t),vy(x,y,t)of stretching obeys the equationsvx(x,y,t)=a(t)x+b(t)vx*(x,y),vy(x,y,t)=a(t)y+b(t)vy*(x,y),where(vx*,vy*)is identical to the two‐dimensional potential flow that satisfies the Cauchy‐Rieman equations in(x,y)coordinates, whilea(t)andb(t)are arbitrary time functions. Drawing on the knowledge of classical hydrodynamics a number of interesting and physically realizable flow fields of uniform thickness film stretching can be predicted analytically by the above solution(vy,vy),which also leads to the analytical proof that thickness uniformity is maintained in any axisymmetrical stretching as long as the film is uniform initially. These findings constitute an important correction to the authors' previous statement that thickness uniformity can be maintained only when the flow field consists of uniform extension inxandydirections expressible by the equationsvx=C11(t)x+C12(t)yandvy=C21(t)x+C22(t)y.