Let \(X^ 0(t)\), \(0\leq t\leq 1\), be a strong Markov process with the infinitesimal generator \[ A^ 0 f= {d(D^ +_ s f)- fdk\over dm},\qquad f\in D(A^ 0)\subset C[0, 1], \] and boundary conditions of Feller-Wentzell-type \[ \kappa_ i f(i)+ (-1)^{i+ 1} \pi_ i(D^ +_ sf)(i)+ \int^ 1_ 0 {f(i)- f(x)\over | s(i)- s(x)|} dq_ i(x)= 0,\quad i= 0,1. \] The author finds the infinitesimal generator and the initial distribution of the process which is the time reversed of \(X^ 0(t)\). Before such problems were considered in the case of local boundary conditions, i.e., when \(q_ i(x)= 0\), \(i= 0,1\).