Distribution queue with Python

Maybe someone can help me or give me a light. I have a list of people's names. Example: "Saulo", "Maria", "Fernando"

I need to create automatic distribution among these people without repeating a person before the list is complete.

Using Python shuffle, it is not certain that the result is always random.

import random

mylist = ["Saulo", "Maria", "Fernando"]
random.shuffle(mylist)

Example: If Saulo receives an item, he will only receive it again when Maria and Fernando receive it too.

Ideas?