I guess it depends on how you understand the definition of morality.
I'd say morality was about judging what is "good" and what is "bad" in human behavior.
The key word there is "judging". Moral judgment is an evolved trait of humans ─ I'd guess of gregarious animals generally.
We humans get our morality in two ways ─ from evolution and from learning. On the evolutionary side, humans show the following moral tendencies ─ dislike for the one who harms, like of fairness and reciprocity, having respect for authority, being loyal to the group, and getting a sense of self-worth through self-denial. We've also evolved a conscience and a capacity for empathy. (I outlined one of the experiments from research
>here<.) You'll notice that those tendencies are capable of conflicting ─ reciprocity vs respect for authority, for example.
The rest of our morality is about social interaction and good and bad manners ─ how to interact with people who are kin, older, younger, same or opposite sex, higher or lower in the peck order, figures of various kinds of authority and so on; how to dine in company, how to excrete politely, how to observe coming of age, pairing, birth and death, and so on.
The thing about all of it is that it makes it possible for humans to live in groups and obtain the advantages of cooperative action, which in evolutionary terms is advantageous to surviving and breeding. And that last-mentioned quality is about as close to "objective" as it gets.