Generate 'n' unique random numbers within a range

I know how to generate a random number within a range in Python.

    random.randint(numLow, numHigh)

And I know I can put this in a loop to generate n amount of these numbers

    for x in range (0, n):
        listOfNumbers.append(random.randint(numLow, numHigh))

However, I need to make sure each number in that list is unique. Other than a load of conditional statements is there a straightforward way of generating n number of unique random numbers?

EDIT: The important thing is that each number in the list is different to the others..

So

[12, 5, 6, 1] = good

But

[12, 5, 5, 1] = bad, because the number 5 occurs twice.

If you just need sampling without replacement:

    >>> import random
    >>> random.sample(range(1, 100), 3)
    [77, 52, 45]

random.sample takes a population and a sample size k and returns k random members of the population.

If you have to control for the case where k is larger than len(population), you need to be prepared to catch a ValueError:

    >>> try:
    ...   random.sample(range(1, 2), 3)
    ... except ValueError:
    ...   print('Sample size exceeded population size.')
    ... 
    Sample size exceeded population size

From: stackoverflow.com/q/22842289