Vertically centering an image with max-height and max-width

I have the following html code:

<div style="border: 3px coral solid;width:400px;height:400px;background:#D4D0C8;">
    <img style="max-width:400px;max-height:400px;" src="myImage.jpg">
</div>

Using these styles images with a width > 400 pixels are resized but remain at the top of the div. Is there some way to vertically center them?