Just because you were rejected the first time you applied for your dream job doesn't mean you can't apply again. The rejection might not have had anything to do with you. Maybe the company filled the position internally, or decided to hold off on filling it for budgetary reasons. Being persistent and working toward the job you want is not likely to burn any bridges. In fact, your persistence might be the key to landing the job the second time around.
Review the job posting again to identify the skills, education, training and personality traits the employer is looking for. Applying for a job means showing the employer you can meet its needs and requirements. Familiarize yourself with all of the requirements so you can show the employer you are a good fit.
Tweak your resume to more closely match what's listed in the job posting. Some companies use applicant tracking systems which filter resumes based on keywords. If you didn't use keywords mentioned in the job posting, your first application might have been rejected for that reason.
Fill out all fields of any online job application materials that the company requires. Along with your resume, some companies use online forms to sort through applications. Not filling out all the information to the fullest -- and not including the keywords specified in the job posting -- could send your application to the slush pile.
Use your cover letter to make your case. If you went through job interviews with the employer before, it's OK to mention it. Just stay positive. Tell the employer why you're so committed to the company and what value you'll bring by working there. In some cases, the employer will appreciate your persistence and commitment to the company. If the job posting mentioned specific skills or traits necessary in the ideal candidate, talk about how you've honed those skills, and what additional experience or training you've gotten since the last time you applied for the job.
Tap into your network to get professional references. For many jobs, it's all about who you know, and one personal connection can help you get your foot in the door. Talk to former colleagues as well as friends, family members, contacts you've made through networking groups and college professors and ask whether they know anyone at the company to which you've applied. See if your connections are willing to make a call on your behalf or talk to a recruiter personally. If not, ask if you can include them on your list of references.
If you still have the contact information for the recruiter or hiring manager with whom you interviewed the first time, contact her and ask for feedback on making your application more attractive to the employer.