Let X and Y be Ito processes with dX$_{s}$ = $phi$$_{s}$dB$_{s}$ ＋ $psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$leq$│X$_{0}$│,│ζ│$leq$│$phi$│, │ξ│$leq$│$psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$leq$│$psi$│ by a more general one │ξ│$leq$$alpha$ │$psi$│ , where a $geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $geq$ 0, extends the work by Burkholder.der.urkholder.der.