Recursive Uppercase Consonants

#include <iostream>
#include <string>
using namespace std;
string uppercaseConsonants(string str, string newstr, int i = 0)
{
   if(isupper(str[i]))
   {
      if(isupper(str[i]) != 'A' || isupper(str[i]) != 'E' ||
         isupper(str[i]) != 'I' || isupper(str[i]) != 'O' ||
         isupper(str[i]) != 'U' && !isspace(str[i]))
      {
         newstr += str[i];
      }
   }
   if(i < str.length()-1)
   {
      return uppercaseConsonants(str, newstr, i + 1);
   }
   return newstr;
}
int main()
{
   string str, newstr = "";
   while(getline(cin, str))
   {
      cout << uppercaseConsonants(str, newstr) << endl;
   }
   return 0;
}