  We have derived the so-called gap equation, which determines the upper
critical magnetic field, perpendicular to conducting chains of a
quasi-one-dimensional superconductor. By analyzing this equation at low
temperatures, we have found that the calculated angular dependence of the upper
critical magnetic field is qualitatively different than that in the so-called
effective mass model. In particular, our theory predicts a non-analytical
angular dependence of the upper critical magnetic field, $H_{c2}(0) -
H_{c2}(\alpha) \sim \alpha^{3/2}$, when magnetic field is close to some special
crystallographic axis and makes an angle $\alpha$ with it. We discuss possible
experiments on the superconductor (DMET)$_2$I$_3$ to discover this
non-analytical dependence.
