I had to do all of the following to completely remove it:
outline-style: none;
box-shadow: none;
border-color: transparent;
Example:
button {_x000D_
border-radius: 20px;_x000D_
padding: 20px;_x000D_
}_x000D_
_x000D_
.no-focusborder:focus {_x000D_
outline-style: none;_x000D_
box-shadow: none;_x000D_
border-color: transparent;_x000D_
background-color: black;_x000D_
color: white;_x000D_
}
_x000D_
<p>Click in the white space, then press the "Tab" key.</p>_x000D_
<button>Button 1 (unchanged)</button>_x000D_
<button class="no-focusborder">Button 2 (no focus border, custom focus indicator to show focus is present but the unwanted highlight is gone)</button>_x000D_
<br/><br/><br/><br/><br/><br/>
_x000D_