Magnetic force microscope (MFM) tips are prepared by coating Si tips of 4 nm radius with L10 ordered FePd-alloy films varying the thickness in a range between 10 and 80 nm. The effects of coating thickness on spatial resolution and switching field of MFM tip are investigated. As the thickness increases from 10 to 20 nm, the MFM signal detection sensitivity is improved and the resolution improves from 12.7 to 7.9 nm. With further increasing the thickness, the resolution decreases due to increase of tip radius. Magnetic bits of 15.9 nm length of a perpendicular medium recorded at 1600 kilo-flux-change-per-inch are distinguishable in the MFM image observed by using a tip coated with 20-nm-thick FePd film. The switching field monotonically increases from 0.70 to 1.50 kOe with increasing the coating thickness from 10 to 80 nm. The present study has shown that it is possible to prepare an MFM tip with spatial resolution better than 10 nm and switching field higher than 1 kOe by coating a sharp Si tip with an L10 ordered FePd-alloy film.