A method to taper the field amplitude in permanent magnet undulators w
ithout changing the undulator gap is presented. It is based on the dev
iations in the field patterns of the magnet blocks produced by the inc
orrect orientation of the magnetization vector. The appropriate arrang
ement of the magnet blocks in the undulator is determined by solving a
set of linear equations obtained using the field values which charact
erize the tapered field profile. The versatility of the method is demo
nstrated by simulating different profile shapes using the same set of
magnet blocks. It is shown that undulator field profiles of required s
hape and size can be obtained by using magnet blocks of proper specifi
cations. The results of the simulations carried out to study the effec
ts of the taper size, profile shape and the undulator gap on the width
s of the distributions of the block magnetization components are prese
nted. As a practical realization of the method a fifteen period long u
ndulator with linearly decreasing field amplitude is assembled. The re
sults of the magnetic field measurements of this undulator are also pr
esented.