Child car safety seat (1, 2), of the type that can be used by a baby measuring 40 cm to 150 cm in size, comprising: - a fixed Isofix base and - a first seat, fixed in a rotary way on the fixed Isofix base, where the first seat is suitable to anchor above a second seat which is smaller size, and where the first seat comprises at least: - one outer casing (10, 7, 8a, 8b, 5, 4) in the form of a seat, comprising a seat, a backrest with sides and two armrests (8a, 8b), and - an inner rigid structure mounted on the fixed Isofix base so that the first seat can rotate with respect to the fixed Isofix base and can be anchored in two different positions: a first position facing forwards and a second position facing backwards, characterised in that the inner rigid structure comprises: - a swivel base solidly attached to an upper structure (6a, 6b) which extends upwards until reaching a part near the back of the first seat, wherein this rigid structure is configured for being mounted in the lower and rear part of the outer casing (10, 7, 8a, 8b, 5, 4) of the first seat, and where the swivel base is configured for being mounted in a rotatory manner on the fixed Isofix base; and - a foldable support leg, which is integrated into the rigid structure, the support leg being height adjustable and hinged at its upper end to one rear part of the upper structure (6a, 6b) of the rigid structure, so that the support leg can adopt two different positions: - an unfolded position when the first seat is facing backwards, in which the support leg is separated from the rigid structure, or - a folded position when the first seat is facing frontwards, in which the support leg is anchored by a lower part to a part of the fixed Isofix base, in such a way that, in this folded position, one inferior part of the support leg remains fixed to the Isofix base and acts as a reinforcement of the rigid structure. - a fixed Isofix base and - a first seat, fixed in a rotary way on the fixed Isofix base, where the first seat is suitable to anchor above a second seat which is smaller size, and where the first seat comprises at least: - one outer casing (10, 7, 8a, 8b, 5, 4) in the form of a seat, comprising a seat, a backrest with sides and two armrests (8a, 8b), and - an inner rigid structure mounted on the fixed Isofix base so that the first seat can rotate with respect to the fixed Isofix base and can be anchored in two different positions: a first position facing forwards and a second position facing backwards, characterised in that the inner rigid structure comprises: - a swivel base solidly attached to an upper structure (6a, 6b) which extends upwards until reaching a part near the back of the first seat, wherein this rigid structure is configured for being mounted in the lower and rear part of the outer casing (10, 7, 8a, 8b, 5, 4) of the first seat, and where the swivel base is configured for being mounted in a rotatory manner on the fixed Isofix base; and - a foldable support leg, which is integrated into the rigid structure, the support leg being height adjustable and hinged at its upper end to one rear part of the upper structure (6a, 6b) of the rigid structure, so that the support leg can adopt two different positions: - an unfolded position when the first seat is facing backwards, in which the support leg is separated from the rigid structure, or - a folded position when the first seat is facing frontwards, in which the support leg is anchored by a lower part to a part of the fixed Isofix base, in such a way that, in this folded position, one inferior part of the support leg remains fixed to the Isofix base and acts as a reinforcement of the rigid structure. - one outer casing (10, 7, 8a, 8b, 5, 4) in the form of a seat, comprising a seat, a backrest with sides and two armrests (8a, 8b), and - an inner rigid structure mounted on the fixed Isofix base so that the first seat can rotate with respect to the fixed Isofix base and can be anchored in two different positions: a first position facing forwards and a second position facing backwards, - a swivel base solidly attached to an upper structure (6a, 6b) which extends upwards until reaching a part near the back of the first seat, wherein this rigid structure is configured for being mounted in the lower and rear part of the outer casing (10, 7, 8a, 8b, 5, 4) of the first seat, and where the swivel base is configured for being mounted in a rotatory manner on the fixed Isofix base; and - a foldable support leg, which is integrated into the rigid structure, the support leg being height adjustable and hinged at its upper end to one rear part of the upper structure (6a, 6b) of the rigid structure, so that the support leg can adopt two different positions: - an unfolded position when the first seat is facing backwards, in which the support leg is separated from the rigid structure, or - a folded position when the first seat is facing frontwards, in which the support leg is anchored by a lower part to a part of the fixed Isofix base, in such a way that, in this folded position, one inferior part of the support leg remains fixed to the Isofix base and acts as a reinforcement of the rigid structure. - an unfolded position when the first seat is facing backwards, in which the support leg is separated from the rigid structure, or - a folded position when the first seat is facing frontwards, in which the support leg is anchored by a lower part to a part of the fixed Isofix base, in such a way that, in this folded position, one inferior part of the support leg remains fixed to the Isofix base and acts as a reinforcement of the rigid structure.