The present invention is directed to methods of preparing linear polymers such as polyalkylene oxides containing a terminal amine in high purity. One preferred method includes reacting a polyalkylene oxide such as polyethylene glycol containing a terminal azide with a phosphine-based reducing agent such as triphenylphosphine or an alkali metal borohydride reducing agent such as sodium borohydride in a solvent to reflux. The resultant polymer-amines are of sufficient purity so that expensive and time consuming purification steps required for pharmaceutical grade polymers are avoided.