  We consider the two-dimensional (2d) random Ising model on a diagonal strip
of the square lattice, where the bonds take two values, $J_1>J_2$, with equal
probability. Using an iterative method, based on a successive application of
the star-triangle transformation, we have determined at the bulk critical
temperature the correlation length along the strip, $\xi_L$, for different
widths of the strip, $L \le 21$. The ratio of the two lengths, $\xi_L/L=A$, is
found to approach the universal value, $A=2/\pi$ for large $L$, independent of
the dilution parameter, $J_1/J_2$. With our method we have demonstrated with
high numerical precision, that the surface correlation function of the 2d
dilute Ising model is self-averaging, in the critical point conformally
coovariant and the corresponding decay exponent is $\eta_{\parallel}=1$.
