The Bagheera mid-engined sports car had proved popular even though it was relatively low-powered and quite expensive for its time. All the motoring press and owners loved it but it was clearly capable of taking more power. In 1980 Matra developed a more modern replacement to cure these and other faults. The first change was a fully galvanised chassis to halt the corrosion that afflicted the unprotected Bagheera chassis. This full immersion hot-dipped galvanising of the whole chassis was another first for Matra. The design was updated to make it cheaper to produce as well as incorporating a more timeless beautifully curved shape that was also very aerodynamic; and the engines were larger and more powerful, giving the higher performance which these cars really deserved. The unique three abreast seating which gave the interior far more room than the average sports car was retained as that had proved popular. Like its predecessor the luggage space was large for this type car, making the Murena an extremely practical sports car.

The Murena, was introduced to the motoring press in September 1980 and was available initially with the Simca 1.6 OHV engine, followed soon after with a 2.2-litre OHC engine, from February 1981. Matra actually wanted the all-alloy 2-litre OHC Douvrin engine from Renault, but they declined its availability, so Matra fitted the new 2.2-litre Simca/Talbot engine developed for the large Tagora saloon. This was the final development of the engine first fitted in the Chrysler 180/2-litre models. It had about the same power as the newer Renault but was heavier with a cast iron block.The 2.2 Murena was well equipped with everything standard including all radio equipment except the set itself which was left open to the customer's choice. The only other extra was metallic paint finish, and yet the car was the equivalent of under £7,000 all taxes paid, which was less than half the cost of similar mid and rear-engined glass fibre sports cars of the time. This was exactly the opposite of the Bagheera which had cost nearly twice the price of equivalent cars of its time.The Murena handled extremely well, taking advantage of the latest 60% low profile tyres. The car was so good that it could obviously cope with, and there was a demand for, even more power, and since the 2.2-litre had been taken from its saloon car role with no modifications, the first upgrade was to offer a dealer fitted performance kit, comprising of both engine upgrades and some bodywork 'aero' modifications. This upgrade carried the title 'Prep 142' after the bhp it produced.

Sales and production of the Murena were just building nicely, when, owing to negotiations with Renault for the Espace, production was halted on request from Renault. Once the contract for the Espace was finalised, and the change of partnership from PSA to Renault formalised, the Murena was to cease production. Matra could use up all the parts and finish all the Murenas 'in the pipeline' but then it was to cease in favour of the Espace. Popular opinion was that the Murena, at less than half the price, was much too good a competitor for the Renault Alpine built at Dieppe, so it was eliminated.Matra had been developing the '4S', a 16-valve engined car to give it even better performance, and at the same time some subtle bodywork improvements to improve air flow for engine, brake cooling, and aerodynamics, but this work had to be dropped with the Renault contract and the agreement to cease production. In the last run of cars Matra built 480 'S' models which were 2.2-litre cars with the 'Prep 142' modifications included during production. A total of only 10,680 Murena were produced during its short 3 year life, just over half being 1.6 models, and a great car was killed off prematurely to satisfy Matra's new automotive partner.