No, the general rule is that "an" is used when the "h" is silent: an hour an heirloom an honor an honest politician
But when the "h" is pronounced, then "a" is used: a home a hand a horror movie a handsome man a hysterical boy a history of my city a hippopotamus a horse a hair
And, Philip's sage advice can sometimes be a bit tricky, as in some parts of North America and Britain, the h is pronounced in a word, where in other parts, it is not pronounced in the same word.
For example, in some parts of the U.S., at least (don't know about other places), the h in humble is not pronounced, while in others, it is. So, you will hear, "That is an humble (pronounced "u