Abstract: A method and apparatus for the prevention of migration of hazardous particulate matter from a negative pressure environment established within a building in order to collect and dispose of the hazardous particulate matter, the apparatus and method for the prevention of migration of a hazardous particulate matter from the area being cleaned including an enclosed passageway positioned parallel of the temporary wall means established so as to define the area to be cleaned, the enclosed passageway being continuously evacuated so as to establish a negative pressure in the enclosed passageway which is greater than the negative pressure in the area being cleaned in order to ensure any hazardous particulate matter escaping from the area being cleaned is captured in the enclosed passageway and removed before migrating to other areas of the building in which normal activities are in progress.