A constraint hydrodynamics algorithm for non-Brownian spherical particles in aqueous systems is developed by applying the RATTLE algorithm to Stokesian dynamics. Hydrodynamic interactions were calculated using far-field grand mobility tensors, and the holonomic translational forces were determined using the time-dependent Lagrange multiplier. The proposed constraint algorithm successfully describes the dynamic motion of a colloidal chain with an initial helical structure under the influences of unidirectional fluid flow and gravitational force.