Two algorithms are in common use for performing molecular-dynamics simulations of fluids composed of molecules with holonomic bond constraints. The SHAKE algorithm is widely used but is conceptually complex. The algorithm of Edberg et al. (EEM), is simple in concept and structure except in regard to the manner in which numerical drift is handled. We describe a simple way of modifying the EEM method so that numerical drift in the holonomic constraints can be treated in a simple non-iterative fashion. The method is applied to fluids composed of planar molecules: liquid benzene and naphthalene. The results for the former system are in agreement with previous simulations using site-site potential models.