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The purpose of this paper is to obtain the bounds on the Higgs mass in the Standard Model for one and two–loops Higgs potential, which includes the contributions of scalar, vector and fermion loops at one –loop and two-loop levels for a bound on the coupling constant λ given in the work of P. Kielanowski and S.R.Juarez W as 0.369 ≤ λ ≤ 0.613. On the basis of these studies, we obtain the upper and lower bounds on the Higgs mass as 143 GeV ≤ mH ≤ 200 GeV. These results will be very useful to LHC experiments for the detection of the Higgs particle and are matching with the results obtained by a few contemporary workers. We also find that the condition for perturbative validity given by Miller is satisfied, when the Higgs mass is calculated perturbatively from the effective potential given by the mass less φ 4 theory at one and two-loop level.