Is it okay to perform Tahajjud after Witir?

Salat Witr is prayed after Salat Taraweeh and Salat Isha in mosque. This the routine followed in the month of Ramadan in my country. If I wake up early and then pray for Tahajjud, Is it okay? I hear that Salat Witir is a cover of Salat, so we can't continue another Salat and then do Witir again, may be because the count of the rakaat must be odd.