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The Halperin-Lubensky-Ma (HLM) effect of a fluctuation-induced change of theorder of phase transition in thin films of type I superconductors withrelatively small Ginzburg-Landau number $\kappa$ is considered. Numerical datafor the free energy, the order parameter jump, the latent heat, and thespecific heat of W, Al and In are presented to reveal the influence of filmthickness and material parameters on the properties of the phase transition. Wedemonstrate for the first time that in contrast to the usual notion the HLMeffect occurs in the most distinct way in superconducting films with highcritical magnetic field $H_{c0}$ rather than in materials with small $\kappa$.The possibility for an experimental observation of the fluctuation change ofthe order of superconducting phase transition in superconducting films isdiscussed.Comment: 11 pages, MikTexTeX, 3 fig, 2 Tables, corrected some typos, Submitted  J.Phys:Cond Ma

New features of the phase transition to the superconducting state in thin films