Method for ultrasonic characterization of a medium in order to locally determine a preferred direction of anisotropy of scatterers in the medium, the method comprising: - a step of generating a series of incident ultrasonic waves (US in) in an area of said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission basis (i); and - a step of generating an experimental reflection matrix R ui (t) defined between the emission basis (i) as input and a reception basis (u) as output; - a step of determining a focused reflection matrix RFoc(r in, r out, δt) which comprises responses of the medium between an input virtual transducer (TV in) of spatial position r in and an output virtual transducer (TV out) of spatial position r out, the responses of the output virtual transducer (TV out) being obtained at a time instant that is shifted by an additional delay 8t relative to a time instant of the responses of the input virtual transducer (TV in), - a step of determining a wavefront image for the input virtual transducer (TV in) and for an additional delay interval, said wavefront image being determined as a function of the speed of sound c 0 in the medium, and said wavefront image being determined based on: - the focused reflection matrix RFoc(rin, r out, δt) and - a ballistic propagation relation of the type δt Δ r out = − sign Δ z out ⋅ Δ r out / c 0, which makes it possible to extract values from the focused reflection matrix in order to construct the wavefront image, and where: δt is the additional delay, |Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δr out = rout - r in, Δz out is the component along a depth axis Z of the spatial position vector Δr out. said wavefront image comprising a focal spot, - a step of determining a preferred direction of the focal spot in the wavefront image by image processing said wavefront image, said preferred direction corresponding to a direction of larger dimension for said focal spot. - a step of generating a series of incident ultrasonic waves (US in) in an area of said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission basis (i); and - a step of generating an experimental reflection matrix R ui (t) defined between the emission basis (i) as input and a reception basis (u) as output; - a step of determining a focused reflection matrix RFoc(r in, r out, δt) which comprises responses of the medium between an input virtual transducer (TV in) of spatial position r in and an output virtual transducer (TV out) of spatial position r out, the responses of the output virtual transducer (TV out) being obtained at a time instant that is shifted by an additional delay 8t relative to a time instant of the responses of the input virtual transducer (TV in), - a step of determining a wavefront image for the input virtual transducer (TV in) and for an additional delay interval, said wavefront image being determined as a function of the speed of sound c 0 in the medium, and said wavefront image being determined based on: - the focused reflection matrix RFoc(rin, r out, δt) and - a ballistic propagation relation of the type δt Δ r out = − sign Δ z out ⋅ Δ r out / c 0, which makes it possible to extract values from the focused reflection matrix in order to construct the wavefront image, and where: δt is the additional delay, |Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δr out = rout - r in, Δz out is the component along a depth axis Z of the spatial position vector Δr out. said wavefront image comprising a focal spot, - the focused reflection matrix RFoc(rin, r out, δt) and - a ballistic propagation relation of the type δt Δ r out = − sign Δ z out ⋅ Δ r out / c 0, which makes it possible to extract values from the focused reflection matrix in order to construct the wavefront image, and where: δt is the additional delay, |Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δr out = rout - r in, Δz out is the component along a depth axis Z of the spatial position vector Δr out. said wavefront image comprising a focal spot, δt is the additional delay, |Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δr out = rout - r in, Δz out is the component along a depth axis Z of the spatial position vector Δr out. said wavefront image comprising a focal spot, - a step of determining a preferred direction of the focal spot in the wavefront image by image processing said wavefront image, said preferred direction corresponding to a direction of larger dimension for said focal spot.