Method 3: Using a Custom Format
One final way you can display negative times, without changing to the 1904 date system and still returning a true numeric value, is to select Home → Cells → Format Cells tab, or right-click and go to Format Cells (pre-2007, Format → Cells). Select the Custom option under Category and use a Custom format of -h:mm.
This method works only if you always want a negative time value displayed. It also requires that you always subtract the earlier time from the later time. This means all times returned really will be positive and will only appear negative.
So, by using any one of these three methods, you will be able to display negative times. Just remember that there are pitfalls to each of them, so always use them with these pitfalls in mind.