The paper is devoted to the convergence of a parallel finite-difference local descent algorithm in global optimization. It is assumed that the objective function is regular and each function evaluation is subject to a deterministic noise. Regular  properties of the objective function are described in terms of parameter set to estimate better the region that algorithm's trajectories converge to. Errors-stability of proposed algorithm is established under suitable conditions. Inspite of errors-stability algorithm considers nondistinct local minima as perturbation and can be effectively applied for solving multiextremal optimization problems. Keywords: gradient method, derivative-free optimization, errors--stability.