The high orbital eccentricity of the planet around 16 Cygni B may have been induced by the companion star, 16 Cygni A, but only if the stellar binary has sufficiently small periastron distance. The long period of the stellar binary, ~3x10^4 yr, implies that less than 1% of the orbit has transpired since its first astrometric measurements in 1830. Therefore, we compute the orbit from the measured instantaneous velocity and position vectors, based on new precise Doppler and astrometric data, along with the Hipparcos parallax. The only unknown parameter is the separation between AB along the line of sight, constrained by the demand that the orbit be bound, which leads to a family of possible orbits for 16 Cygni AB. The physically plausible orbits have 18,200 yr<P<1.3 Myr, 877<a<15,180 AU, and periastron distances 68<r_p<1500 AU. The orbit is definitely eccentric, with e=0.54-0.96. All orbital parameters here are in approximate agreement with the previous computation by Romanenko. The new stellar binary orbit remains consistent with the possibility that perturbations from 16 Cygni A cause the eccentricity in the planet around 16 Cygni B. Recently a red point source has been detected 3.2" from 16 Cygni A, but its membership remains unknown (Trilling et al.). We assess its membership based on astrometry and velocities of 16 Cygni A. The point source is either a low-mass M dwarf separated by ~80 AU from component A or it is a higher mass star of perhaps ~0.5 M_solar, separated by at least 150 AU from 16 Cygni A-indeed possibly a background star. If the new companion is bound, 16 Cygni A and B never approach each other closer than ~500 AU, which diminishes the prospects that 16 Cygni A induces the eccentricity of the planet around 16 Cygni B.