The exact eigenfunction solution of diffraction by a plane angular sector is improved. Previous work on the problem has used the continued fraction method, and results have only been presented for the quarter plane. The continued fraction method requires computation times that become unreasonably long for larger eigenvalues due to instability in the method. A method which overcomes all these difficulties is described. Results are shown for eigenfunctions and eigenvalues on angular sectors of various shapes. Results for the current distribution and the far field are also shown.