In recent years, in order to enhance the safety and durability of motor vehicles and to reduce the fuel consumption of vehicles, it has become very necessary to use a high strength cold rolled steel strip, especially, galvanized, having a tensile strength of from 35 to 50 Kg/mm.sup.2, as inner and outer panels of motor vehicles.  In order to apply the galvanized steel strip to the above-mentioned uses, it is indispensable that the steel strip exhibits not only a high tensile strength but also a superior deep drawability which allows the steel strip to resist to a severe press-forming procedure. 
Generally, the hot galvanized steel strip is produced by using a continuous galvanizing line wherein the steel strip is subjected to an in-line annealing, for example, the Senzimir type galvanizing line.  In the case of the in-line annealing, the annealing time is short and the heating and cooling rates are high.  Therefore, it is known that the production of a high strength galvanized steel strip having excellent deep drawability is difficult.  Usually, a high strength galvanized steel strip is produced for a structural use, containing, a strengthening alloying component consisting of carbon and manganese.  However, this type of high strength galvanized steel strip exhibits a poor deep drawability and, therefore, is unsuitable as inner or outer panels for motor vehicles which must be subjected to a deep drawing procedure. 
In most recent years, as a method for producing a high strength deep drawing galvanized steel strip, a rephosphorized Al-killed steel is box-annealed for a long period of time, and then, processed by the in-line annealing type continuous galvanizing line.  However, in the above-mentioned method, the advantage of the in-line annealing procedure cannot be obtained and the product becomes very expensive. 
Japanese Patent Application Publication (KOKOKU) Nos.  42-12348 (1967) and 44-18066 (1969) disclose a cold rolled steel strip having excellent deep drawability, respectively.  These steels are very low carbon steels with titanium added. 
Also, it is known that phosphorus is a cheap strengthening alloying element for steel strips. 
However, hitherto it is believed that the addition of phosphorus to the titanium-containing very low carbon steel causes the recrystallization temperature to rise and the deep drawability to lower, and, therefore, should be avoided. 
Under the above-mentioned circumstances, it was strongly desired by the industry to provide a new type of high strength cold rolled steel strip which exhibits a superior deep drawability.