  An n \times n matrix A has a normal defect of k if there exists an (n+k)
\times (n+k) normal matrix A_{ext} with A as a leading principal submatrix and
k minimal. In this paper we compute the normal defect of a special class of 4
\times 4 matrices, namely matrices whose only nonzero entries lie on the
superdiagonal, and we provide details for constructing minimal normal
completion matrices A_{ext}. We also prove a result for a related class of n
\times n matrices. Finally, we present an example of a 6 \times 6 block
diagonal matrix having the property that its normal defect is strictly less
than the sum of the normal defects of each of its blocks, and we provide
sufficient conditions for when the normal defect of a block diagonal matrix is
equal to the sum of the normal defects of each of its blocks.
