Nonreflecting stationary sets in Pκλ

Let κ be a regular uncountable cardinal and λ⩾κ+. The principle of Stationary Reflection in Pκλ has been successful in settling problems of infinitary combinatorics in the case κ=ω1. For κ⩾ω2 the principle is known to fail if λ is large enough. In this paper the principle is shown to fail for every λ⩾κ+.