Get a list of accounts based on a record type

I have this code: that is generating a list of accounts for an "Account" Field  in a Visualforce Page. I would like it to generate a list of Accountst that have REE record type. Currently it shows Accounts of other record types than REE. Can I have some ideas of what I am doing wrong? 

//Method to get the Account List drop down
    public List<SelectOption>getAccountOptions() {
    ID rtAccount = Account.sObjectType.getDescribe().getRecordTypeInfosByName().get('REE').getRecordTypeId();       
        System.Debug('getAccountOptions Start');
        //Execute query to get the respective roles
        System.debug('<<<<<<< Get Account List Method Started >>>>>>>');
        List<SelectOption> options = new List<SelectOption>(); 
       for(Account acc: [SELECT ID, Name FROM Account WHERE RecordTypeId= rtAccount LIMIT 200]) 
        {
            options.add(new SelectOption(acc.Id,acc.Name));
        }
        System.debug('<<<<<<< Get Account List Method Completed >>>>>>>');
         System.Debug('getAccountOptions End');
        return options;
    }