C# Splitting strings randomly

I have a string like this:

string str = "ABCDEFGHI"

I want a result like:

string str1 = "AB";
string str2 = "CDEF";
string str3 = "G";
string str4 = "HI";

The idea is to randomly partitioning a string into a sequence of substring with random length.

I've tried the following:

public static string SplitString(string input)
    {
        string result = "";
        int j = 0;
        for (int i = 0; i < input.Length; i++)
        {
            Random random = new Random();
            j = random.Next(i+1, input.Length);
            string subString = input.Substring(i,j); //ERROR
            i = j-1;
            Console.WriteLine("New substring: " + subString);
            result = result + subString;
        }
        return result;
    }

It looks like this approach is not correct at all, because when I create a substring and the i index is greater than the j, the program goes in exception.

Is there a way to avoid this error?