The transport and relaxation properties of a molecular supercooled liquid on an isobar are studied by molecular dynamics. The molecule is a rigid heteronuclear biatomic system. The diffusivity is fitted over four orders of magnitude by the power law [formula presented] with [formula presented] and [formula presented] The self-part of the intermediate scattering function [formula presented] exhibits a steplike behavior at the lowest temperatures. On cooling, the increase of the related relaxation time [formula presented] tracks the diffusivity, i.e., [formula presented] At the lowest temperatures, fractions of highly mobile and trapped molecules are also evidenced. Translational jumps are also evidenced. The duration of the jumps exhibits a distribution. The distribution of the waiting times before a jump takes place, [formula presented] is exponential at higher temperatures. At lower temperatures a power-law divergence is evidenced at short times, [formula presented] with [formula presented] which is ascribed to intermittency. The shear viscosity is fitted by the power law [formula presented] with [formula presented] at the lowest temperatures. At higher temperatures the Stokes-Einstein relation fits the data if stick boundary conditions are assumed. The product [formula presented] increases at lower temperatures, and the Stokes-Einstein relation breaks down at a temperature which is close to the one where the intermittency is evidenced by [formula presented] A precursor effect of the breakdown is observed, which manifests itself as an apparent stick-slip transition. © 2001 The American Physical Society.