two-) fold degenerate due to symmetry, the number of one-electron states whose levels are located in the neighborhood of $\varepsilon_{\mbox{\scriptsize F}}$ is considerable. Since such a feature is known to enhance the SC pair correlation functions in the two-chain Hubbard model \[\] even in strongly correlated situations, this feature is considered to bring about the remarkable increase of the energy gain. Although the particular peaking location of $t'$ may be slightly size-dependent since the one-electron levels are size-dependent, such a concentration of one-electron levels around $\varepsilon_{\mbox{\scriptsize F}}$ is considered to occur for any system size when the appropriate negative $t'$ pushes down the van Hove singularity close to $\varepsilon_{\mbox{\scriptsize F}}$. Therefore, this effect should work even in the bulk limit.

Electron-Density Dependence
---------------------------

Figure \[fig:gain-r\] shows the energy gain per site in the SC state as a function of the electron density $\rho = N_e/N_s$ for the cases of $t' = 0, - 0.10$ and $-0.15$. The corresponding values of $\Delta$ as a function of $\rho$ are exhibited in Fig. \[fig:D-r\]. When $t' = - 0.10$ whose curve is exhibited with closed circles, the cases of $\rho = 0.68, 0.76, 0.84$ and $0.92$ have an open shell, in another word, 