A discrete growth model with a restricted curvature constraint is investigated by measuring both the surface width and the height difference correlation function. In our model, where an extremal height is suppressed, the surface width W shows the roughness exponent alpha approximately 0.561 and the dynamics exponent z approximately 1.69 in one substrate dimension. However the correlation function has an unusual scaling behavior and produces different wandering exponent alpha(') approximately 1.33 and its dynamic exponent z(') approximately 4. The discrepancy is due to the fact that the correlation length increases with a power law t(1/z(')) until it reaches the value proportional to Ldelta at time t(s) approximately L(z), where L is the system size and delta is the "window exponent" satisfying the relation delta=z/z(')=alpha/alpha('). delta is a new exponent to characterize the window size of the system.