Assembly of sash-frame and leaf of a door, window or the like, said assembly including a locking fitting such as a lock, an espagnolette, an espagnolette-lock or the like, comprising: - a keeper the sash-frame is provided with; - at least one locking organ the leaf is provided with and subjected to elastic restoring means in the locking position, in order to cooperate, when closing said leaf against the sash-frame, with the keeper; - means for locking the locking organ or organs in the unlocked position when the leaf is partially opened, these locking means including an actuating finger designed capable of cooperating with an unlocking stop associated with the sash-frame for controlling the unlocking of said locking means during the closing of the leaf against the sash-frame; - adjusting means defined capable of adjusting the relative positioning of said unlocking stop relative to said operating finger, wherein: - the adjusting means: - are of a discrete type; - include indexing means, on the one hand, for allowing said actuating finger and/or said unlocking stop to occupy at least two different positions, as the case may be, on the leaf or on the sash-frame and, on the other hand, defined by indexing means associated with the unlocking stop and/or the actuating finger and designed capable of cooperating with complementary indexing means; - are designed capable of permitting the adjustment in a direction perpendicular to the plane of the leaf and/or of the sash-frame, respectively, of said actuating finger and/or the unlocking stop, respectively; - the unlocking stop is mounted: - on the sash-frame through a fastening bracket including the complementary indexing means; - at the level of a first end, hinging on the fastening bracket so as to be capable of pivoting about a vertical axis perpendicular to the plane of the fillister of the sash-frame and to the direction of adjustment, said unlocking stop including at a second end said indexing means capable of cooperating with complementary indexing means said fixing bracket is provided with. - a keeper the sash-frame is provided with; - at least one locking organ the leaf is provided with and subjected to elastic restoring means in the locking position, in order to cooperate, when closing said leaf against the sash-frame, with the keeper; - means for locking the locking organ or organs in the unlocked position when the leaf is partially opened, these locking means including an actuating finger designed capable of cooperating with an unlocking stop associated with the sash-frame for controlling the unlocking of said locking means during the closing of the leaf against the sash-frame; - adjusting means defined capable of adjusting the relative positioning of said unlocking stop relative to said operating finger, wherein: - the adjusting means: - are of a discrete type; - include indexing means, on the one hand, for allowing said actuating finger and/or said unlocking stop to occupy at least two different positions, as the case may be, on the leaf or on the sash-frame and, on the other hand, defined by indexing means associated with the unlocking stop and/or the actuating finger and designed capable of cooperating with complementary indexing means; - are designed capable of permitting the adjustment in a direction perpendicular to the plane of the leaf and/or of the sash-frame, respectively, of said actuating finger and/or the unlocking stop, respectively; - are of a discrete type; - include indexing means, on the one hand, for allowing said actuating finger and/or said unlocking stop to occupy at least two different positions, as the case may be, on the leaf or on the sash-frame and, on the other hand, defined by indexing means associated with the unlocking stop and/or the actuating finger and designed capable of cooperating with complementary indexing means; - are designed capable of permitting the adjustment in a direction perpendicular to the plane of the leaf and/or of the sash-frame, respectively, of said actuating finger and/or the unlocking stop, respectively; - the unlocking stop is mounted: - on the sash-frame through a fastening bracket including the complementary indexing means; - at the level of a first end, hinging on the fastening bracket so as to be capable of pivoting about a vertical axis perpendicular to the plane of the fillister of the sash-frame and to the direction of adjustment, said unlocking stop including at a second end said indexing means capable of cooperating with complementary indexing means said fixing bracket is provided with. - on the sash-frame through a fastening bracket including the complementary indexing means; - at the level of a first end, hinging on the fastening bracket so as to be capable of pivoting about a vertical axis perpendicular to the plane of the fillister of the sash-frame and to the direction of adjustment, said unlocking stop including at a second end said indexing means capable of cooperating with complementary indexing means said fixing bracket is provided with.