Does removing items from a C# List<T> retain other items' orders?

Lately, I've been writing a lot of code that looks like this:

List<MyObject> myList = new List<MyObject>();
...
for(int i = 0; i < myList.Count; ++i)
{
  if(/*myList[i] meets removal criteria*/)
  {
     myList.RemoveAt(i);
     --i;  //Check this index again for the next item
     //Do other stuff as well
  }
}

and I just became a little paranoid that maybe List doesn't retain object order at removal. I don't know the C# spec well enough to know for sure. Can someone verify that I either am or am not asking for trouble with this pattern?

EDIT: Perhaps I should clarify that the above is a very simplified example and more things happen if the item needs to be removed so I don't think List<T>.RemoveAll() is terribly applicable here. Although it is a nice function. I have added a comment in the if() block above to specifically mention that.