Get rid of the old version
# yum remove ImageMagick
Install the dependancies
# yum install wget tcl-devel libpng-devel libjpeg-devel ghostscript-devel bzip2-devel freetype-devel libtiff-devel
Now get ImageMagick from http://www.imagemagick.org/script/download.php and download the latest source with wget or curl.
Extract it
# tar zxvf ImageMagick-x.x.x-x.tar.gz
Build it
# configure --prefix=/usr/local --with-bzlib=yes --with-fontconfig=yes --with-freetype=yes --with-gslib=yes --with-gvc=yes --with-jpeg=yes --with-jp2=yes --with-png=yes --with-tiff=yes
# make clean
# make
# make install
Then you should be hot to trot. Type
convert -version
to see the upgraded version number.