With the help of the Boussinesq perturbation expansion, a new basic equation describing the long, small-amplitude, unidirectional wave motion in shallow water with surface tension is derived to fourth order, namely a higher-order Korteweg-de Vries (KdV) equation. The procedure for deriving this equation assumes that the relation between the small parameter , which measures the ratio of wave amplitude to undisturbed fluid depth, and the small parameter , which measures the square of the ratio of fluid depth to wave length, is taken in the form , where is a small, dimensionless parameter which is the order of the amplitude of the motion. Hirota's bilinear method is used to investigate one- and two-soliton solutions for this new higher-order KdV equation.