One way is to open a recordset object with VBA and iterate through the recordset. Every fourth record you grab the unique identifier and run an append query to another table.
Another way is to create an new empty table with the same structure as your original, but with the addition of an autonumber field (Named NewIdentifer for this example). Use an append query and send all the records into this new table. This will create a new list with a sequential record number for each record and with no omissions.
All you do now is create a select query that returns all the fields you need with a 'where clause' similar to 'WHERE Table1.NewIdentifer/4 = INT(Table1.NewIdentifer/4)'. Translation: when the value of the autonumber field can be divided by 4 and return a remainder of zero you have the fourth record.
* The where clause is essentially a substitute for the MOD function. It will work for all versions of Access. I'm not entirely certain but if you're using Access 2002 onwards and you have the 'Microsoft Office 10.0 Object Library' referenced then you should be able to use the MOD function eg 'MOD(NewIdentifier,4) = 0'
Anyhow have a play and see how you go.