Hmmm, you sure you're not getting eggs confused with something else? Almost all animal protein is "complete" it's the vegetable protein that can be missing amino acids.
From Wikipedia -
"Complete protein (or whole protein) is a protein that contains all of the essential amino acids for the dietary needs of humans or other animals. [1]
Common dietary sources of protein include meats, eggs, grains, legumes, nuts, and dairy products such as milk and cheese.[2] Animal sources of proteins have the complete complement of all 8-10 essential amino acids. Certain vegetable sources also contain all 8-10 essential amino acids. However, many plant sources, while not entirely void, lack one or more amino acids in large enough quantity to be considered a complete source of protein. A variety of complete proteins in the diet are one way of assuring that the body's amino acid needs are met. Complete proteins are not necessary for this, however. All the essential amino acids can be obtained on their own from various everyday plant sources, which, contrary to popular belief, do not need to be combined in the same meal according to many health organizations
Sources of complete protein:
* Complete proteins can be found in animal foods, including meat, poultry, seafood, eggs, and dairy.
* Some plant and microbial sources also contain complete proteins, including spirulina, quinoa, soy, buckwheat, hempseed, and amaranth, among others. "