Can you make a contraction of "should not have"? If you can, how would you write it?

I always hear people saying shouldn't've, but I don't know if it's correct?
You can say "shouldn't have," but not "shouldn't've." Or at least, not officially. Because people tend to clip their words, it is possible that when people say "shouldn't have," it sounds like "shouldn't've." I myself probably do this often, especially when I talk quickly. But it would be incorrect to write it like that.
beware of students using, and yes, actually writing, shouldn't OF, for shouldn't HAVE. the same goes for wouldn't OF/HAVE. as explained by kitkattail, this is a transliteration of rapid, or "clipped" speech. i came upon this problem as a french teacher while i was teaching hypothetical (if/then) structures. english and french have nearly identical structures with regard to hypothetical sentences, but i actually had english native speaker students at a well-respected major university argue that the following sentence was correct: "if i would of had the money, i would of taken a trip". the "clipping" not only causes the erroneous OF to take the place of HAVE (i.e. spoken quickly, "would of" and "would have" sound similar), but the similarity between the contractions i+would (i'd) and i+had (i'd) led to confusion between the two. when i explained that the correct form of the sentence, with no contractions is "if i had had the money, i would have taken a trip", this caused another uproar, as some incredulous students refused to believe that HAD HAD could be correct. cries of "that sounds wierd" were riposted by me: "better to sound 'wierd' than ignorant"!
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i am a lousy typist, nothing weird (or wierd) about that! mea culpa...
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The answer then would be" If I had had the money I would have taken a trip".
They thought "had had" was weird? Really? But people say that all the time! I don't understand!
written, and spoken slowly, it does have a bit of an odd ring to it. young, inattentive speakers of english are wont to question all sorts of things... at least here in the states.
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