leaving off last job on resume

Leave the 4-month job off your resume and don’t worry.

The new employer will research the past jobs, not the 4-month trial.

My sole caution: make sure that your references do not mention the 4-month job and confine their remarks to your work with them/their organization.

The best approach is to be upfront and honest. In all likelihood a new employer or recruiter will find out anyway (they probably do a background check, or at least should). I wouldn't worry to much about leaving after only a short time; employers are much more used to seeing that--and accepting it--than they used to be. You don't have to go into a lot of detail as to why you're leaving. I recommend approaching your resignation very professionally, as uncomfortable as that might be, and letting your supervisor and human resources know in person. All of it will reflect well on you, even if your departure comes at a difficult time for them. Should a future employer call your current supervisor checking references, you would want them to be able to report that you handled the situation well.