The well-established PIF-01/S1/P43 picosecond streak tube, designed 30 years ago and still manufactured at the A.M. Prokhorov General Physics Institute, was modified by replacing its traditional P43 phosphor screen with a P47 one having approximately three orders of magnitude shorter decay time. The experimental measurements of this decay time were provided by PIF-01/S1/P47 image tube photocathode irradiation either with a single or a train of 8 ps laser pulses separated by 8 ns from each other at a 1.08 μm wavelength. The results of our preliminary measurements of P47-BH phosphor (manufactured by Phosphor Technology Ltd) indicate the possibility of employing the PIF-01/S1/P47 streak tube for synchrotron diagnostics at a units megahertz repetition rate without the negative influence of ‘ghost images’ from the previous streak records.