Combine apples and water to cover in a large stock pot. Bring to a boil. Reduce heat; cover and cook 15 minutes or until apples are tender. Drain. Press apples through a sieve.
Combine apple pulp and fruit pectin in a large stock pot. Bring to a boil; cook 1 minute. Stir in sugar and cinnamon. Reduce heat; simmer, uncovered, stirring occasionally, 1 hour or until thickened.
Spoon apple jam immediately into hot, sterilized jars, leaving 1/4-inch head space; cover at once with metal lids, and screw bands tight. Process in a boiling- water bath 10 minutes.