Cut the foliage off the hyacinth within 3 inches of ground level with shears. Remove the foliage only after it dies back on its own in early summer.
Loosen the soil around each hyacinth plant. Lift the bulbs out of the soil.
Trim the dead roots off the base of the main bulb. The bulb produces new roots in fall and winter to replace the old, dead ones.
Inspect the bulb for offsets, which resemble smaller full bulbs. Large offsets are closer to maturity.
Twist the offset gently until it snaps off the main bulb. Leave the smallest offsets on the bulb to continue maturing and remove only the largest ones.
Replant the original bulb and the removed offsets. Plant the bulbs so the bottom sits 6 inches beneath the soil surface. Space the bulbs 4 to 6 inches apart.