In this paper, we study base-normality and total paracompactness 
of subspaces of products of two ordinals. 
We prove the following: 
(1) For every regular cardinal $\k$ with $\k\geq\o_1$, 
there exists a normal non-base-normal subspace $X$ of 
$(\k+1)^2$ with $w(X)=\k$. 
(2) If $A$ and $B$ are subspaces of an ordinal, 
then $A\times B$ is base-normal if and only if $A\times B$ is normal. 
(3) Every normal subspace of ${\o_1}^2$ is base-normal. 
(4) Every paracompact subspace of products of two ordinals 
is totally paracompact.