How can I remove subrecord in mongoDB

I have a database looking like that:

{
    "_id": ObjectId("50525e55467f67da3f8baf06"),
    "client": "client1"
}{
    "_id": ObjectId("505262f0deed32a758410b1c"),
    "client": "client2"
}{
    "_id": ObjectId("505269e2062dae91946e3c26"),
    "client": "client3"
}{
    "_id": ObjectId("5052f469341bdc4e8ac1b226"),
    "client": "client4",
    "products": [
        {
            "name": "product1"
        },
        {
            "name": "product2"
        }
    ]
}

My question is, how can I remove product2 from the product list of client4 without removing the client4 record? The output should look like this:

{
    "_id": ObjectId("50525e55467f67da3f8baf06"),
    "client": "client1"
}{
    "_id": ObjectId("505262f0deed32a758410b1c"),
    "client": "client2"
}{
    "_id": ObjectId("505269e2062dae91946e3c26"),
    "client": "client3"
}{
    "_id": ObjectId("5052f469341bdc4e8ac1b226"),
    "client": "client4",
    "products": {
        "name": "product1"
    }
}