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In this paper, we use the lower and upper solution method to obtain an existence theorem for the fourth-order boundary-value problem $$displaylines{ u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)),quad 0<t<1,cr u(0)=u'(1)=u''(0)=0,quad u'''(1)=gig(int^1_0u''(t)dheta(t)ig), }$$ where $f : [0,1]imes mathbb{R}^4 o mathbb{R}$, $g : mathbb{R}o mathbb{R}$ are continuous and may be nonlinear, and $int^1_0u''(t)dheta(t)$ denotes the Riemann-Stieltjes integral.