An antiquated way of saying ないis to use ぬ. If you know how to form the plain negative form of Japanese verbs, simply take of that ないand replace it with ぬ. You can hear this in many enka songs, for example, one of my favourites here. One part of his lyrics are 届かぬなら (if it doesn't arrive). If we take this apart you can see how it's been formed is just like the ないform you are so used to. (The plain form of 届かぬ is 届く.)
Using ぬ instead of ない can also make your words sound more polite, the way speaking with old-fashioned words does in English. Here is a line from ひとつのタブー by Hoshi Shinichi, using the Xないようにお願いする form which you will often hear in trains, etc (Please don't leave anything on the train = お忘れ物のないよう、お願いします). In this case, the line says ｢あわてたりなさらぬよう、お願いします」. I would translate it as something like "Please remain calm", or "We ask that you please remain calm". I guess you can break it down as "We ask that you conduct yourself so as not to panic and the like." Notice that the sentence is made more polite by the use of the keigo form of suru, which is nasaru.