How can I prevent my fixed div from overlapping my other divs

I'm making a website for my world history class and I am attempting to make a heading for the website. Unfortunately, the heading overlaps the first paragraph. Is there any way I can fix this without changing the position? I need the position to be fixed. This is the html for the header:

<div id="menu">
<a href="#about">About</a>
<a href="#donatello">Donatello</a>
<a href="#michelangelo">Michelangelo</a>
<a href="">Martin Luther</a>
<a href="">Henry VIII</a>
<a href="">Mary Wollstonecraft</a>
<a href="">Francis Bacon</a>
<a href="">Isaac Newton</a>
<a href="">Galileo Galilei</a>
<a href="">Marquis de Lafayette</a>
</div>

This is the css:

#menu{
padding:30px;
background:#000;
border:5px solid #000000;
border-radius:0px;
position:fixed;
z-index:1;
right:0px;
left:0px;
top:0px;
text-align:center;
}

Thank you for the help.