A well-known Scharfetter-Gummel (SG) scheme for convection-dominated problems of semiconductor and gas discharge plasmas is improved. A one-dimensional convection-diffusion equation is considered. It is shown that the original SG scheme is accurate if the potential drop between two adjacent nodes is much less than the electron temperature. To satisfy this condition a pair of additional nodes between adjacent nodes are inserted. The distance between these "virtual" nodes can be choosen small enough to obtain flux at the cell bound with the high accuracy. The number densities at virtual nodes are found by interpolation. Tests have shown that the accuracy of this scheme is comparable to the FCT technique, but in contrast it does not produce a "staircase" disturbance on rapidly changing functions.