No, it does not become haram when prepared by a non-Muslim.
There are five simple conditions that must be met for meat to be considered halal. I have pages of discussion and notes on this, so permit me to summarize:
- Intelligence: He has to understand and intend to slaughter, on purpose. (This excludes accidental/unintentional slaughtering.)
- Religion: He has to be a Muslim, or a Christian, or a Jew. No other religion.
- Instrument Used: It must be slaughtered by a sharp tool, such as a knife. No blunt objects, bludgeoning, stunning to death, etc.
- Cut the four veins: There are four "veins" that make up the "perfect" cut -- esophagus, two jugular veins, and trachea. There's a difference about if you don't get all four.
- You must say "bismillah" (in the name of Allah/God Almighty) before slaughtering. Yes, even if you're a Christian or Jew.
Notice there is no condition #6 that says that "you must always have Muslim eyes on it until it reaches a Muslim house," or anything similar.
In fact, we know cases where rasulullah ate at the house of a Jewish man or a woman (the latter being after the conquest of Khaybar). Think about this. He walked into an invitation in the house of a non-Muslim in a non-Muslim land and ate their food. So subhanallah, we see that Islam is easy, from the best of the best of the best.
If you're interested in more, deep details, please open more questions. There are differences of opinion (and tons of details) about the five conditions and the implications from madhab to madhab.