CSS: On hover show and hide different div's at the same time?

Here is CSS example how to show hidden div (on hover):

<div class="showhim">HOVER ME<div class="showme">hai</div></div>

and

.showme{ 
display: none;
}
.showhim:hover .showme{
display : block;
}

Can I show one div and hide another one at the same time by using only CSS? Here is example how to use JS for this purpose: http://jsfiddle.net/joshvito/GaZQ6/