A simple, fully covariant generalisation of the DBI action to the non-abelian case is proposed. The non-abelian degrees of freedom are incorporated by adjoining to the (bosonic) worldvolume of the brane a number of anticommuting fermionic directions corresponding to boundary fermions in the string picture. The proposed action treats these variables as classical but there is a straightforward interpretation in terms of matrices. The gauge-fixed action is shown to be in agreement with the Myers action derived from T-duality. It is also shown that the requirement of covariance in the above sense leads to a modified WZ term which again agrees with Myers.