We present direct mass measurements of the short-lived ⁴⁴V, ⁴⁸Mn, ⁴¹Ti and ⁴⁵Cr nuclei. A novel experimental method has been used that is based on projectile fragmentation, in-flight separation of relativistic heavy ions with the fragment separator (FRS), and on isochronous operation of the experimental storage ring (ESR). A mass resolving power of 110000 (FWHM) and an accuracy of about (100-500) keV has been achieved. The impact of the present results on the rp-process in X-ray burst models is discussed.