I add a new geometry column to the "mad" table so I could update it with the polygons from an Intersection with the polygons of the table "clip".
Since my database is huge an it was taking a lot of time to comput I opt for this solution "Getting intersections the faster way" (http://postgis.net/2014/03/14/tip_intersection_faster/). These SELECT worked for me but I wanted to do an UPDATE. I tried using this command:
UPDATE mad SET geom_p=CASE WHEN ST_CoveredBy(mad.geom,clip.geom)
THEN mad.geom
ELSE ST_Multi(ST_Intersection(mad.geom,clip.geom)) END AS geom FROM mad AS mad
INNER JOIN clip AS clip
ON (ST_Intersects(mad.geom,clip.geom) AND NOT ST_Touches(mad.geom,clip.geom)));
ERROR: syntax error at or near "AS"
LINE 1: ...(ST_Intersection(mad.geom,b.geom)) END AS geom FR...