Yes, look at the instant PayPal Prepaid Notification (IPN) - https://www.paypal.com/ipn/
This will cause POST of transaction data to be sent to you whenever a transaction has been started. If you are currently using the Website Payment Standard (HTML buttons), you can simply add
<input type="hidden" name="notify_url" value="http://full-URL-to-the-script-you-set-up-for-IPN">
POST, PayPal, cmd = _notify-validate https://www.paypal.com/cgi-bin/webscr ( https://www.sandbox.paypal.com/cgi-bin/webscr ), IPN-.
INVALID VERIFIED.
INVALID , POST IPN PayPal, VERIFIED , POST IPN PayPal.