Edit in JSFiddle

$("#click-button").on('click', firstClick)

function firstClick() {
    alert("First Clicked");
    $("#click-button").off('click').on('click', secondClick)
}

function secondClick() {
    alert("Second Clicked");
    $("#click-button").off('click').on('click', firstClick)
}

<input type="button" id="click-button" value="Click Me" />