  We compute the upper bound on the mass of the lightest Higgs boson in the
Minimal Supersymmetric Standard Model in a model-independent way, including
leading (one-loop) and next-to-leading order (two-loop) radiative corrections.
We find that (contrary to some recent claims) the two-loop corrections are
negative with respect to the one-loop result and relatively small ($\simlt
3$\%). After defining physical (pole) top quark mass $M_t$, by including QCD
self-energies, and physical Higgs mass $M_H$, by including the electroweak
self-energies $\Pi\left(M_H^2\right)-\Pi(0)$, we obtain the upper limit on
$M_H$ as a function of supersymmetric parameters. We include as supersymmetric
parameters the scale of supersymmetry breaking $M_S$, the value of $\tan \beta$
and the mixing between stops $X_t= A_t + \mu \cot\beta$ (which is responsible
for the threshold correction on the Higgs quartic coupling). Our results do not
depend on further details of the supersymmetric model. In particular, for
$M_S\leq 1$ TeV, maximal threshold effect $X_t^2=6M_S^2$ and any value of
$\tan\beta$, we find $M_H\leq 140$ GeV for $M_t\leq 190$ GeV. In the particular
scenario where the top is in its infrared fixed point we find $M_H\leq 86$ GeV
for $M_t = 170$ GeV.
