Starting with investigating the Haar scaling function

the scaling coefficient function is first presented.Then the Battle-Lemarié basis is extended to the generalized Battle-Lemarié basis by introducing time-shift factor to the scaling coefficient function of the Battle-Lemarié.The rationality of the extending method

which is used in this paper

is theoretically proved.Some basic properties of the generalized Battle-Lemarié basis are also discussed.Our research results show that all the Battle-Lemarié bases inherit many good properties of the original Battle-Lemarié bases

such as orthonormality

time frequency localization

exponential decay and so on.Meanwhile a series of neoteric symmetric multiresolution analysis basis are generated.The generalized Battle-Lemarié wavelets are better than the corresponding original Battle-Lemarié wavelets in regularity.