It sounds like the palm may have a magnesium deficiency. This is a common problem in Florida palms, and especially in Canary Island Dates. It appears first on the oldest leaves and progresses up through the canopy.

Symptoms include a broad, light yellow band along the margins of the older leaves with the center of the leaf remaining green and in severe cases, the leaflet tips may die.

Fortunately, this deficiency is rarely, if ever, fatal. The leaves demonstrating the symptoms will never recover and must be replaced by new healthy ones. A regular fertilization program (4 times per year) using an 8-2-10 or 8-2-12 analysis fertilizer, supplemented with magnesium sulfate, should control the problem.

Additional Resource
http://edis.ifas.ufl.edu/EP273