Eliminate Duplicate Charecters

string greet = "happynewyear";

            string result = string.Empty;

            List<char> lstchars = new List<char>();

            for (int i = 0; i < greet.Length; i++)

            {

                char c = greet[i];

                if (!lstchars.Contains(c))

                {

                    lstchars.Add(c);

                }

            }

            foreach (char c in lstchars)

            {

                result += c;

            }

            Console.WriteLine(result);

            Console.ReadLine();