  A new immersed finite element (IFE) method is developed for second-order
elliptic problems with discontinuous diffusion coefficient. The IFE space is
constructed based on the rotated Q1 nonconforming finite elements with the
integral-value degrees of freedom. The standard nonconforming Galerkin method
is employed in this IFE method without any penalty stabilization term. Error
estimates in energy and L2 norms are proved to be better than $O(h\sqrt{|\log
h|})$ and $O(h^2|\log h|)$, respectively, where the logarithm factors reflect
jump discontinuity. Numerical results are reported to confirm our analysis.
