This catalog contains the proper motions of 1535 Basic FK5 stars (Cat. ) derived from a direct combination of the Hipparcos catalog with 6 compiled and 57 observational ground-based astrometric catalogs. We used the positions and parallaxes from the HIP (Cat. ), radial velocities from the HIC (Cat. ) and positions from 57 observational ground-based catalogs with the mean epochs from 1939 to 1995. The differences of RA and DEC in the sense of `observational catalog minus HIP at the observational catalog epoch' were calculated and approximated by Legendre-Hermite-Fourier functions which then were eliminated. Thus formed the series of star positions referred to the ICRS for the various epochs were used to derive the new proper motions. The proper motions from the HIP and ground-based compilations GC, N30, FK5, N70E, CMC9 and KSV2 (Time Service Catalog 2) reduced to the Hipparcos system were used for the calculation of mean weighted proper motions as initial values for the first iteration of the main procedure. The resulting proper motions keep the proper motion system of Hipparcos (this is an advantage of the PMFS proper motions over ground-based ones such as from the FK5) but they are individually independent from any other proper motions, such as HIP, FK5, FK6, etc. The advantage of the PMFS proper motions over HIP ones is that they reflect the star motions over decades, not only in the course of the mission. Namely, the non-linear motions of 134 stars were directly separated into their proper motions of the barycentres and periodical motions of the photocentres around barycentres, and the proper motions of some other 200 stars were separated from their non-linear motions which were implicit in large differences between the PMFS and HIP proper motions of the stars. The stars were classified into 760 single ones, 187 astrometrically wide pairs, 35 astrometrically close pairs for which the results are doubtful and 551 stellar systems with 553 brighter components in the Basic FK5 for which the astrometrically observed photocentre moves, or can move, non-linearly with an amplitude >1 mas (including almost all known visual, photocentric and spectroscopic orbital pairs). Thus, the PMFS proper motions are the ones of the barycentres of these stars and stellar systems. The median precision of the proper motion components is 0.5 mas/year for proper motion on RA and 0.7 mas/year on DEC. Details are can be found at http://www.geocities.com/georgegontcharov/