Theoretical investigation of an infinitely long Goubau line or Cylindrical Dielectric Coated Conductor (CDCC) is presented here. Literature survey shows that the CDCC has been investigated for fundamental transverse magnetic (TM) and transverse electric (TE) mode only. In this work, the contributions of TE and TM modes are utilized to find the solution of different HEM modes. Theoretical results are verified with earlier published work. Modal charts are given here for εr = 20 and 38.