Let be the following one-dimensional threshold diffusion model : dX(t)=b(X(t)-ro)dt+dB(t) We consider the case when b is Lipschitz continuous on R and 0 is a threshold for its first derivative; b' is continuous on R* and the right and left limits in 0 are finite, but different. We want to estime ro from discrete observations of the stationary ergodic solution process, (X(k*h_n), k=0,...,n), as n*h_n goes to infinity and h_n goes to 0. For that purpose, we introduce the least squares estimator based on the approximate discrete-time Euler's scheme. This estimator is consistent. Moreover if n*(h_n)**3 goes to 0 , we prove that it is asymptotically normal with a standard rate.