No, you can't.
Say that the samllest item is 15, the largest is 83 middle item is 56. that's the same as saying "If 50 is less than 56, search between 56 and 83" In a sorted list (it MUST be a sorted list, and I'm assuming a standard, ascending sort), the search would never find the target.
Now,technically, you could do a descending sort. In that case,if 50 < middle, you would search right, but not left. But the standard is to do an ascending sort.
No matter which you use, the keys are these: it has to be a sorted list and the decision has to select the correct side of the midpoint where the target must be, if it is there at all.