As the model of CR geometry, the Heisenberg groups H_n play the same roles as Euclidean spaces to the Riemannian geometry. The essential problem we ask is that if the fundamental theorem of curves still holds in the Heisenberg groups. Due to the contact structures of H_n, we consider the horizontally regular curves and show that the answer is positive. We also define the concept of orders for such curves to distinguish if the curves are "spacial" or "plan". We show that two curves with the same order differ from a rigid motion if and only if they have the same invaritnats: p-cuarvatures and contact normality. Thus, combining with our previous work, we complete the classification of horizontally regular curves in the Heisenberg groups. 

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