Laminin 521, a heterotrimeric glycoprotein composed of one alpha 5, one beta 2 and one gamma 1 chain, is a defined matrix for feeder-free culture of human embryonic (hES) and induced pluripotent (hiPS) stem cells. When used in combination with defined maintenance media, Laminin 521 reliably facilitates self-renewal of human hES and hiPS cells without spontaneous differentiation.