We use a dual-laser optical-tweezers (DLOT, Smith et al., Science, 271:795, 1996) to define the highly cooperative conformational transition in the molecule of DNA, where the natural B-DNA is converted into a new overstretched conformation called S-DNA (Bensimon et al., Phys. Rev. Lett. 74, 4754, 1995; Cluzel et al., Science 271, 792, 1996). Single molecules of double stranded λ-phage DNA are stretched at 27 °C with the DLOT either with ramp length changes or with force step staircases. The microchamber solution contains 150 mM NaCI, 10 mM tris-HCl, 1 mM EDTA, pH 8.0. When the DNA molecule is stretched in length clamp mode, it shows the previously described highly cooperative overstretching transition at ∼60 pN, attributed to unwinding from the B-form to the 1.7 times longer S-form. Stretching the molecule in force clamp mode with a staircase of force steps (ΔF, step size1-5 pN) at 5 s intervals shows different amount of DNA elongation (ΔL) for a given clamped force F depending on ΔF The peak of the Gaussian fit to the ΔL-F relations is at ∼60 pN independently of the step size, but the σ of the Gaussian is smaller at smaller ΔF. The L-F relations obtained by integrating the Gaussian curves,fitted with the Hill sigmoid equation, show a Hill coefficient n (an estimate of the order of the underlying transition) that increases with the reduction of ΔF. n is 20, 70 and 125 with ΔF = 5, 2 and 1 pN respectively. These results demonstrate the importance of fine force clamp to establish the degree of bps cooperativity for the unwinding of DNA helix. Supported by MiUR, Ente Cassa di Risparmio di Firenze (2007. 1421) and ITB-CNR (Milano).