How to build unique random couple from a single list

I want to find random couples on a single list with different members.

Here is my code:

import random

def alea_couple(members):
    couples = []
    for p in members:
        possibles = [r for r in members if r!=p and r not in [elem[1] for elem in couples]] 
        couples.append((p, random.choice(possibles)))
    return couples

my_members = ["member1", "member2", "member3", "member4"]
random.shuffle(my_members)
alea_couple(my_members)

[('member2', 'member1'),
 ('member3', 'member4'),
 ('member1', 'member3'),
 ('member4', 'member2')]

I am sure there is a better way and more elegant way to do this with itertools.combinations

do you have a piece of advice ?