We use a modified method of the apparent motion parameters (AMP), in which the initial data from the Gaia DR2 catalog are not only high-precision coordinates, parallaxes, and radial velocities of the components of the studied wide binary stars, but are also their proper motions. The coincidence of the AMP orbits obtained both from the Gaia DR2 data and from the Pulkovo series from 1960-2019 leads to an orbit that is unambiguous in terms of an ascending node. The results for improving the orbits of such visual binaries of the Pulkovo research program as ADS 246, 2757, 10386, and 12169 are presented. Orbits (with periods of 1226, 1075, 4500, and 4900 years), orbital orientation parameters in the Galaxy coordinate frame, and the masses of these systems are obtained (0.59+/-0.05, 1.7+/-0.3, 1.7+/-0.4, and 2.25+/-0.5M_{sun}_). It is shown that dense homogeneous series of ground-based observations, such as CCD observations with the 26-inch refractor of the Pulkovo Observatory, do not lose their relevance, serve as the basis for identifying the best solution based on both Gaia data and our own observations, and should be continued. It was also shown that the Thiele-Innes method is not suitable for determining the orbits of binary stars with a separation of more than 100AU.