The short wave theory was used to obtain the second approximation, called the β-approximation, for the parameters of one-dimensional shock waves. In this approximation, at the higher-order terms of the expansion of functions in power series, the coefficients do not coincide with the second derivatives of the functions in their argument, but provide significantly the best match with the true values of the functions. Comparison of calculations based on the obtained solution with the results of numerical calculations for a flat shock wave with a triangular profile in air shows that this approximation, when calculating the shock wave parameters, including the duration of the compression phase, allows extending the short wave theory applicability range with an error of a fraction of a percent to an overpressure at the front 0.3, and within a few percent — up to 0.4 of the initial pressure in the atmosphere.