1) Click into “design” and into “edit html/css”
2) Click on “main_style.css” to open the css editing page
3) Here locate this code:

#search-button {
float: right;
padding-left: 15px;
cur

Different theme may have different code details. The important part here is to locate this #search-button . Anything below the identifier code is not important.

For MILO Theme users, the all-in-one themes have its own search bar customization area. Please SCROLL to near the bottom of the page to locate this code:

/* ------------------------------------------------------------------------------/
Search Bar
/ ------------------------------------------------------------------------------ */
#search-button {
display: table-cell;
}

4) Here add display: none; like this:

#search-button {
display: none !important;
float: right;
padding-left: 15px;

5) Save your change and publish your site